In your situation, what is important to prove partnership is that you, the couple, have a private space within the family home, particularly a shared sleeping space. This is to show that the partner is not just an informal visitor or lodger. So you need to show evidence, maybe by letters from the home-owner(s) and by regular visitor(s) who have seen your set-up and maybe been entertained there, of what the exact arrangements are for your accommodation. Also, as you say you don't have separate bills for utilities, it would be good to show how you both contribute to the household expenses - maybe a regular payment from your bank.