There's two kinds of joint ownership of real estate, by two people.In one , one joint owner automatically becomes sole owner on the death of the other ('joint tenancy') In the other the parties are both owners of a share each in the property , each share being whatever they agree ("tenancy in common"). The difference is important.
http://www.swarb.co.uk/lawb/cvrJointTenancy.sh tml
gives an explanation.
In the end you'll have to do whatever the mortgage lender wants, if they allow it at all, as already explained above.