Not sure if this has all been pointed out before but I just read this:-
www.lawontheweb.co.uk/family_law/cohabitation
If you read it from the perspective of your EXP, there isn't much to gain comfort in it.
"However, their (co-habiting) relationship with one another is not recognised as having any legal standing, and they have no special status in the eyes of the English legal system....
If you have just been living together then you should be aware that there is no such thing in English law as a "common law wife" (or husband for that matter). If you live together and your relationship breaks down then it is each man or woman for themselves." 
It goes onto say that to protect himself, your ex should have:-
- Made sure the house was in joint names nope-
- Set up a simple Cohabitation/Living Together agreement nope
- Made joint wills did you?
Then it says if the above wasn't done, he might have a case if you'd made an agreement (but he'd have to prove it), contributed financially or put up some money towards the deposit no, no, no
Anything else will be extremely expensive and time-consuming to address through the courts... but he's broke
So, the advice you are getting here is very good... drag it out, push his costs up and leave your lawyer to get on with it.