As Meaghan27 indicates, if there's any form of charge against one or both of the properties (such as a mortgage), things can get tricky. For example, if there's a mortgage, it will almost certainly be 'joint and several', meaning that the lender is free to pursue either party for their money if the need arises. A lender would probably be unlikely to accept the transfer of such a mortgage into a single name, as it would mean that there was then only one person that they could chase for their money.
However if there are no mortgages, all that's needed is for a couple of deeds of transfer to be drawn up, a couple of copies of form TR1 to be submitted and then all of those documents to be sent to the Land Registry, together with the appropriate fees.