Anglian Air Centre is a good school, but I would go and pay them all a visit. Its not like they are far apart and its always best to look for yourself to see if you get a good feeling about the place.
The class 1 medical aspect is obviously extremely important if your goal is just to go down the commercial route. If you aren't going to get a PPL if you can't get a class 1 medical, then finding out about that aspect would be my priority. I am pretty sure that you can download the eye test limits/tolerances etc from the CAA website. If you give this to your optician, they should be able to give a pretty good indication of whether they think you would pass the eye test for a class 1 before you part with £300 plus of hard earned!
You are right that there is not a lot going on in East Anglia by way of commercial flight training. Stapleford is the closest and has a good reputation. But if you are going to stay away for the week whilst doing a cpl/ir, you might as well drive 3 or 4 hrs instead of 2? So don't let distance restrict you from going to the best school for you.
Briefly, you need a 'frozen' ATPL to get employment with an airline. A fATPL is really just CPL/ME/IR/MCC (with 14 ATPL Theory exam passes)which becomes unfrozen when you have 1500 hrs. There is more to it than this, but thats it roughly!
Good luck and let us know how you get on!