It depends. It is one of the least complex transactions. Some people might well manage it. Mind you, if it is simple transaction, it should not be dear to go to a solicitor.
A mortgage means that the property is effectively owned by another party and there can be no dealings with the property without their consent. They can either be joined in the Transfer ( very tedious as most lenders do not want this aggravation ) or else, its often a good opportunity to re-mortgage i.e. transfer, redeem first mortgage and put second mortgage in place in joint names - all at the same time.