A couple of the venues you mention in Britain have been used for cycling.Apart from the purpose-built cycling circuits at Krylatskoye Ring and Izu, however, I can't name any that were built fully for cycling, and safety concerns and changes in logistics have meant that the sprawling, extensive motor racing circuits of sufficient length to make a cycling circuit that isn't going to see half the field lapped are few in number now.
There are a number of occasions in the past where the World Championships have used motor racing venues - I may have missed one or two but I think this is comprehensive:
Where a motor racing venue comprised the entire course: 1927 Nürburgring, 1954 Solingen (Klingenring), 1960 Karl-Marx-Stadt (Sachsenring), 1965 San Sebastián (Circuito Lasarte-Oria), 1966 Nürburgring, 1969 (amateurs) Brno (Masaryk Ring) and 1978 Nürburgring.
Where a circuit incorporated the motor racing venue for start/finish but also used surrounding roads to extend course/add obstacles: 1958 Reims-Gueux, 1959 Zandvoort, 1968 Imola, 1969 (professionals) Zolder, 1970 Leicester (Mallory Park), 1973 Barcelona (Montjuïc Park) and 2002 Zolder.
Where a circuit did not start/finish at a motor racing venue but nevertheless incorporated part of it within the course: 1962 Salò di Garda and 1982 Goodwood.
Of those courses where a motor racing venue comprised the entire course, the Nürburgring is the only one which is a permanent road course, not one which utilized public roads. The Klingenring and Circuito Lasarte-Oria have long since passed into disuse, while the Sachsenring has been reprofiled like Spa-Francorchamps into a shorter course, and a brand new permanent facility has been built in the 1980s within the confines of the old Masaryk-Ring, so the roads are still there but the amenities have all gone to the new course. Of the courses where the motor racing venue was incorporated, Reims-Gueux and Montjuïc Park were street circuits which have since passed into disuse, Salò di Garda was a motorcycle street circuit which was different to the Worlds course but included some of the same stretches, while Zandvoort has been significantly shortened and extensively reprofiled since, leaving just Imola, Zolder and the two British venues (neither of which are in regular use anymore for competitive motorsport, though the latter retains its stands for the Goodwood Festival of Speed, a heritage event). The Imola circuit has been resurrected twice in the Giro in recent years and Zolder can raise money from selling stand seating for its cyclocross events to supplement any interest in road.
Purpose-built motor racing venues are simply not of sufficient length to host major event type bike racing other than as a stage finish, and I'm not sure you could really justify the expenditure of paying for grandstand seating if you're only going to see the riders come by once for a sprint finish such as, say, Motorland Aragón in the Vuelta in 2012; Laguna Seca at least got some time gaps, but even so the action was at the top of the hill, into the Corkscrew, not at the finish line. Everywhere else that paid stands and paid fan zones have been implemented - Richmond, Box Hill and so on - the riders have passed multiple times and the sites have either been the known decisive part of the course or the finish (and realistically if we're getting fans to pay for stadium seating at a motor racing venue, it's going to be the finish). I know that the Ronde van Vlaanderen has had some success with getting paying customers for only seeing the action two or three times on the Paterberg and Oude Kwaremont, but that's in a race with >100 years of history and those being already-established iconic locations. Similarly to Laguna Seca, you could have finishes at circuits with significant elevation change that has the opportunity to create an exciting final few kilometres, such as İstanbul Park, Autopolis, Portimão, Red Bull Ring or Road Atlanta - the latter of which was also used in the Tour of Georgia to host a time trial - which is also frequently what motorsport courses are used for in stage racing, such as Miller Motorsports Park in the Tour of Utah or TT Circuit Assen in the Vuelta in 2009 - though both of these have their drawbacks as options for driving the profitability potential of staging a race (if the stage just finishes at the circuit, it's hard to justify the expenditure if you only see the riders once, and while a TT lets you see all the riders, it's also the most limited as a spectacle for the audience when it is viewing from a distance as it would be up in the stands).
Reasonably-speaking, to host a stage race you would not want to have a circuit so short that people are getting pulled from the course for getting lapped (imagine surviving a 40-minute time cut in the mountains, then being eliminated for being lapped on a 3km circuit in a flat stage), and likewise to host a one-day race of the highest level you'd want a reasonably long circuit (I think for a championship of any real level, 11-12km is the minimum), and there are no fully permanent motor racing courses of that length nowadays. The Nürburgring is the exception, as it always has been, but everything else is either incorporating a mix of permanent and temporary facilities, such as the Le Mans Circuit de la Sarthe, temporary in extremis, such as the Isle of Man Mountain Course, or has either been reprofiled into a shorter course (Sachsenring, Spa-Francorchamps, Schleizer Dreieck, Charade) or fallen into disuse (Reims-Gueux, Pescara, Schottenring, Solitudering). Interlagos might hold the Copa América de Ciclismo, but there we're talking a pretty small-scale event. Likewise, short flat circuits are not such a problem in short stage races that don't really have any history or prestige, such as the Yas Marina Circuit in the Tour of Abu Dhabi, at least if they're the final stage. We have seen them in some longer ones, but not with any great effect (Barcelona-Montmeló in the Volta a Catalunya, for example).
As a result, you'd have to look at that second group, courses where you could incorporate part of the current permanent facility along with the roads surrounding the area to create a challenging course. Spa is a perfect opportunity because while the course was reprofiled in the late 1970s, it was still partly public roads from Stavelot through Blanchimont to La Source, and then from La Source through Eau Rouge-Radillon and down the Kemmel Straight until the mid 2000s, and so the connection to the old Spa course is still there, and you could have a Worlds/Euros championship race on the old Spa circuit as a result. Imola, as we know, still offers those opportunities and with differing numbers of circuits provides different results - the two winners in recent Giri there have been Ilnur Zakarin and Sam Bennett, not especially similar rider types! Another great example would be the Mount Panorama Circuit in Australia, although that's technically fully a street circuit; it's just over 6km long, but connects fully to the town of Bathurst outside it - however the section of circuit that you'd skip would be the home straight, with the stands in it, which rather limits the usefulness of the course for driving income from sale of grandstand seating! Circuit de la Sarthe would work for this, as the full course is 13,6km in length, but it is however predominantly flat. The Circuit de Charade is perhaps more suited, but even then, while we could extend from the present 4km circuit to the old course which was very hilly and technical in the Puys of the Auvergne, it was still only 8km in length and would require some extension - after all, there do remain some legacy circuits which are up in the 7-8km range which could feasibly be options if we were going to accept that as a distance - Spa's new layout is 7km, Road America is 6,5km, and Potrero de los Funes is 6,3km, all of which feature significant elevation changes and could produce some interesting racing, what with Road America's uphill dart to the line, and Potrero's set of switchbacks finishing 1km from the line.
Other options are of course being explored elsewhere - the 2020 Olympic Road Race will incorporate Fuji Speedway, postponing the Super GT 500miles of Fuji for the season, meaning there will be no "true" endurance race in the Super GT season next year, unfortunately, with the 1000km Suzuka falling out of their jurisdiction now. The circuit designed looks interestingly hilly, although the unnecessary and somewhat insulting disparity between the complexity of the men's and women's races has drawn much-deserved criticism, with the organisers and the UCI falling on the old Tour of California trick of claiming that the height metres compensates for a lack of selective obstacles - though I'm not sure why they wouldn't just use the Izu facility as that always generates good racing and would certainly merit the entrance fee to sit in the grandstands more than the speedway, which will only see the men twice mid-race and then once at the finish.
A lot of modern facilities do not have the direct connection to the outside roads that enable them to be used with that connectivity that Imola, Zolder, Goodwood and so on have had, but there are definitely possibilities out there. Le Castellet (Circuit Paul Ricard) could make an interesting stage finish in Paris-Nice or the Tour, located as it is in hills between La Ciotat and Toulon, and Mugello's location in the Apennines with its proximity to the Passo del Giogo, the Passo della Futa and Colla di Casaglia among several smaller climbs makes it a very enticing proposition also. In Britain, the Brands Hatch circuit in Kent would be close enough to London to attract a good crowd and presumably be much cheaper than closing central London roads for the Tour of Britain - the circuit is short but it has tarmacked entry and exit points and is in a range of small hills similar to those used in the London Olympic Road Race. Spain held stages of the Volta a Catalunya at Montmeló, and Circuit de Navarra at Los Arcos has hosted the Vuelta a couple of times, but both are in relatively geographically uninteresting areas of otherwise promising race locations. The Autodromo Internacional de Algarve in Portimão would be promising for the Volta ao Algarve or maybe a Portugal (I did consider it for a prologue of the Vuelta in a prospective Race Design Thread design) because it has a lot of elevation changes - all only 200m or so in length but it's a real rollercoaster of a motor racing circuit, worse than Sonoma or Inje Speedium. It could also appear as a finish directly off a descent of the Serra de Monchique/Foia climb that has been used in the Volta ao Algarve in recent years - though a circuit introducing that would be around 40-50km in length.
Some more complex street circuits could be incorporated into longer circuits around the surrounding area potentially, a bit like the Monaco ITT in the 2009 Tour de France. These areas frequently utilise temporary seating, although some, such as the Norisring in Germany, use existing stanchions. Even so, the infrastructure to bring in that temporary seating is there, so it would be relatively doable. The Pau street circuit includes a steep but short climb and is renowned as a technical challenge for drivers, while Macau's Guia Circuit is the stuff of legend. The recent fad for part-permanent, part-temporary circuits, borne out of (often oil-rich) countries trying to buy themselves some popularity with a glamorous location trying to feed off of what people love about other people's circuits, offers other possibilities, such as Singapore's Marina Bay Street Circuit and the Baku Street Circuit which has some similarities to the course used for the 2015 European Games Road Race.
Brands Hatch and the roads around it were the venue for the Paralympic Cycling in 2012 - Zanardi returning to win medals.
The 2017 British Championships used the Mountain Course on the Isle of Man - 2 laps and then a local circuit in Douglas for the men.