Even if she hadn't paid part of the deposit, contributing towards the mortgage and other household costs since the beginning will give her the right to claim
a form of constructive trust over the property, giving her cause of action to sue you for part of the proceeds of sale. The amount she could be awarded could depend entirely on which of you the judge likes the most, or whatever you agree to settle for.
As you've already agreed an amount though, it's a bit of a moot point unless you decide to renege on your deal. You've made a great sounding offer, and she'd be a bit mad not to take it as if she wants to play hardball and wants you to sell, she runs the risk of getting significantly less (which you say is the probably outcome) or even nothing at all if you simply refuse to sell.
Getting her sign a document relinquishing all claims over the property would be a good idea. You don't necessarily need a solicitor to do it for you though. Just get an impartial third party to sign as a witness (or, in the absence of anyone impartial, get one of your mates and one of her mates to jointly witness) so neither of you can later try and deny it's validity.