No deed of gift necessary.
Whether you hold as joint tenants or tenants in common depends on how you want your respective halves of the property to be inherited - likley to be as tenants in common to leave things as flexible as possible, then ensuring your respective wills do what they need to do.
So if no deed of gift is necessary can this be done diy?
I have had a look at tr1 and it looks straighforward. The main thing is to state that there is no money exchange.
I'd rather avoid a convenancying fee earner if possible, the last one we used forgot to register a property at LR.......