15 man squad:
Cook/Trott/Lyth
Ballance/Bell/Root
Ali/Stokes/Rashid
Buttler
Anderson/Woakes/Plunkett/Wood/Mills (Broad needs some serious time off if he's gonna make it past another two years in international cricket)
Possibly take Panesar instead of Rashid or a seamer, and a spare keeper instead of a seamer.
Team:
Cook, Trott, Ballance, Bell, Root, Stokes, Ali, Buttler, Plunkett, Anderson, Mills. Rashid in for Stokes if it's a spinning deck, Woakes likely to play ahead of Mills. Lots of bowling though so I'd play Mills and just use him as a shock weapon.
Realistically though, the team will be almost identical to the last test of last summer. This is the ECB after all, and in fairness we did well against India.