Slightly further West there is Henlow Flying Club. They have a very well maintained collection of Cessna's and Piper's and a relaxed kind of atmosphere. Its a civil operation, not military, although based at RAF Henlow.
I'm a student at Cambridge Aero Club and they seem a pretty good outfit, although I've never been a student elsewhere so don't have anything to compare to. They don't charge landing fees which at first glance makes the prices seem competitive with MASF.
But as others have said you should pick somewhere convenient as you will be going there a lot (for me Cambridge airport is ~10 minutes drive from home and ~5 minutes from work).
A simple price comparison between Conington Flying Club, Mid Anglia School of Flying and Cambridge Aero Club tells me Conington would be my choice. From personal experience - the high price doesn't mean anything other than high overhead costs! Who wants to pay those??
You may also wish to consider where you will continue to fly after your training not only in terms of prices, but also club facilities and atmosphere. Again, on this, Conington would be my choice.
Wherever you end up getting airborne; best of luck and enjoy it!
Not knocking anyone in the area, but I've flown at a few of the establishments mentioned.
The standard of instruction was fine at all of them.
However, I made the choice to pay a little more based on the fleet. I fly well equipped modern aircraft where everything works, and I've never had a cancellation because an aircraft has gone tech.
I really do understand that every pound spent on flying is really tough on a lot of people - it was for me for many, many years (it took me five years to get my PPL way back because I really couldn't afford it).
But I would suggest that if you can afford it (a big if, I do understand), fly the best fleet you can. You'll enjoy it so much more.
There are a lot of old, tired airframes out there that are perfectly safe, but you'd never want to drive a car with such knackered interiors and ancillaries that just dont work.
I fly well equipped modern aircraft where everything works
It's not quite the case that absolutely everything works at Cambridge Aero Club - you might get an aircraft with the EGT gauge not working.
Apart from the EGT gauge, it's almost always the case that all the kit is working, and that you won't for example turn up for a planned IFR flight to find that the only aircraft left on the ground are ones with half the avionics out of service.