I am not sure David is right. What he says is correct if you are both living together in the same house and the other house is empty or let out. In your case you are both in the same position as a couple who are married, but separated. You are both living alone and independently supporting your own homes from your own incomes. It would probably be worthwhile checking the situation out with a solicitor.
I agree with Grandetante over wills. Less sure about having joint bank accounts. The problem with joint accounts is that when you sort out Powers of Attorney you both have to have the same Attorneys to be able to access each others bank accounts. We got caught out by this. My Aunt and Uncle, who were childless, both chose different attorneys but the accounts could be accessed only if they had a minimum of one attorney in common, which they didn't, so we had to go through a difficult process of getting one of them to change their Attorney to one that the other also had and then cancel one PoA and negotiate (and pay) for a new one.