If it's a joint mortgage (i.e. both names are actually on the deed) then you should have no issue with getting some of the equity from the house. Even if your name isn't on the deeds, I'm pretty sure that there is precedent where if one party has been contributing to the upkeep of the house (utility bills etc) but not the actual mortgage payments, they are still entitled to an equal share of the equity post split.
As such, I see no reason why you can't ask for half of the equity in the house (minus the cost of deed transfer / solicitor fees etc).