Download form TR1, and the associated notes, from here:
http://www.landregistry.gov.uk/
(Click 'Forms/Publications' and then 'Forms')
You'll probably also need some of the 'proof of identity' stuff as well. Read the notes to form TR1.
Basically, as long as you hand over the money and complete the necessary Land Registry paperwork, that's all there is to it. (With a 'normal' house purchase you'd need to carry out the 'searches' first but you might have already committed yourself beyond that point anyway. Otherwise the local council can help you check, for example, that there's no new dual carriageway due to go through the middle of the house!).
The only point at which you might have to use a solicitor is for the 'proof of identity' bit. When I sold part of my garden to my neighbour, a couple of years ago, I had to get a local solicitor to look at my passport and sign a document stating that I really am me! She only charged me five quid.
Chris