To finally answer the OP's post...
I will accept any England player if the new coach can get them performing in their game plan, except maybe Calum Clark. It's easy to say "Get rid, not good enough, they failed", but the coaches failed them (and they failed them back) and another coach could change a lot. The difference in Ireland under Kidney and Schmidt is a good example of that.
However, I'd be really worried by any coach that looked at Brad Barritt or Dylan Hartley as mainstays.
Barritt simply because I don't want to see a very negative style and it would lead to undue criticism of the regime, win or lose. I'm not asking for King Carlos style tactics but there has to be a demand for exciting rugby.
Hartley is because you can't trust him and he doesn't offer enough to compensate for that in my opinion. I don't want to tell coaches what to do but equally I don't think anyone who accepts Hartley's indiscipline is right for the job and I don't think anyone who can't find another hooker is either.
The following players have been underperforming for a while and it would be a surprising level of up-turn for them to be good enough although sometimes needs must (imo)
Tom Wood - Seems to have lost his speed and power
Alex Corbisiero - *gigantic sigh*
Alex Goode - Not quick enough or physical enough
Next category are those who clearly can contribute at international level but have pretty major gaps in their game that will make it difficult for them
Chris Robshaw - No gas
James Haskell - No brain
Nick Easter - Is a zombie, although arguably better for it
Ben Youngs - Sketchy tekkers, tendency to crab, still our best scrum-half
Richard Wigglesworth - No break, takes forever to shift the ball
Danny Care - No kicking game
Owen Farrell - No spontaneity
George Ford - Questionable composure and defence
Luthor Burrell - Softest big lad around
Billy Twelvetrees - Flustercluck machine
Sam Burgess - Sam Burgess
Mike Brown - Worry list of big game flubs, no distribution
Now we have the guys who have the ability and no real gaps but are in such god-awful form that they're on offer anyway
Joe Marler - It's a scrum deal
Mako Vunipola - Ditto
Dan Cole - Ditto
Kieran Brookes - Ditto
Tom Youngs - Ditto, with throwing, although that's exaggerated
Rob Webber - Throwing
Courtney Lawes - Scrum, maul, lineout calling
Geoff Parling - Scrum... wait, why have I just named nearly every tight five forward
Ben Morgan - Probably not fit. Boo.
I think that's it.
So... basically, Launchbury, Bunipola, Joseph and the wings are safe, and everyone else should be considered vulnerable (mainly unknown quantities not considered). A lot of them will be back though.