Quite a complicated one this, and bit of a minefield !
Your friend has put up the 'downpayment' - they should expect a return on this pro rata to the increase in the property's value.
(eg. if the property originally cost �100,000, and they put up �10,000 (10%), and it is revalued at / sold for �150,000, then they can expect to receive �15,000 return on their investment.
Secondly, the money they paid in renovations has made it habitable and enabled you to live there, and also added value to the property itself.
Thirdly, since your partner put down a 'downpayment', the amount you have had to borrow (ie the mortgage), and the resulting repayments you have made are actually less because of the money they have invested in the original purchase.
They could also argue that they have lost out on potential rental income because you have been living there.
You don't actually say what proportion of the money they put up, in who's name the mortgage is in, or whether you had any form of agreement in place. I would get some advice and try and work it out amicably with your friend.