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Unless it is going to be truly finacially beneficial for you to sell part of the garden to the neighbour, I would advise against it- it may well put off prospective Buyers and therefore hamper any Sale.
Even though it may only be a small piece of land, any Transfer would have to be dealt with like any otherhouse purchase- namely, a Land Registry Transfer will need to be prepared by a Solicitor, to include a Land Registry compliant plan showing the exact dimensions of the land to be sold. This Transfer will need to be registered
at the Land Registry, which process is likely to take a good few weeks. Only once the Transfer has been registered has the land legally been transferred to the neighbour.
Any Buyer of the main property will not therefore wish to exchange Contracts until this registration has been completed.
The Transfer document for the garden land will need to be prepared by your Solicitor- you will be advised for example, to put a covenant in the Transfer preventing your neighbour from building on this land. The Transfer may also need to show who is responsible for erecting and maintaining any new fence.
Your Solicitor is likely to charge at least £500 plus VAT for the work involved and the neighbour will also need to instruct their own Solicitor- despite it only being a small piece of land, you will see form the above that it is still quite involved. A Surveyor is likely to charge £300 to prepare the Land Registry compliant plan.
I hope this assists and set sout the legal position.