You will have to get your house deeds changed to remove the bit of land from them, create new deeds for the piece and also get the Land Registry entries updated. Thus the little bit becomes a separate piece, in its own right, with its own deeds and LR entry. You then sell this.
With some research on the web, you could perhaps do it yourself, but IMO, when your house is involved, I'd let a solicitor do it.
You're probably looking at a few �100 costs, which (as they want you to do it) the buyer should be paying. As to the value, in real terms not much, but obviously it's worth whatever they are willing to pay. Have they suggested a price yet? FWIW, if it could only be of use as garden, I'd have guessed a few �100s.