As Bobbins has said - Brailsford is not a coach in the sense of training a rider, and Ellingsworth had never coached Wiggins, according to Wiggins, until 2010.
In his book, Ellingsworth does not mention training or coaching Wiggins once - in fact they held UK team training camps for the World champs in 2009 and Wiggo didn't even show up. You'd think someone who had coached a rider to 2009 4th place at the Tour, then elevated to the podium (his book was released in 2013) would mention at least once training Wiggo to that podium, but no, nothing.
We don't know who coached Wiggo in 2009, and for that matter, neither does Jonathan Vaughters, the team manager / owner of Wiggins' 2009 Tour team.
Vaughters also claimed Wiggo was being trained in Manchester, but unless that's corroborated somewhere, he could have been anywhere.
You know that makes sense.