I am sure you may know this but some schools have a very close relationship with certain airlines. If you do the FI/CPL/IR with them they may help to get you past the sifting stage.
I can think of one but I think the condition was that you needed to do the Ppl with them too.
Yes indeed.
In terms of established reputation Stapleford seem like a good bet in the London area. A large school with an attached AOC operation and a commercial operator based at the airfield (LEA have a couple of Kingairs based there). definitely one I will be investigating.
Flying Time at Shoreham also look good. My only concern is that they are a relative newcomer whereas Stapleford has been around for yonks.