Question Author
Thanks for all of the replies.
The relevant neighbour's house is actually behind mine, as we live in a square block of 4 one-bedroomed houses, so that everyone has one neighbour next door to them and one neighbour behind them,
The existing fence between our gardens doesn't (as would seem logical) run at a right-angle to our common side wall. Instead, it goes off at an angle, effectively giving me what would logically seem to be a chunk of 'his' garden. He simply wants to straighten it up, so that he will be able to fit an extra shed into his garden. It's unlikely that the value of my house would be affected, since the change would simply bring my garden back to a 'proper' (i.e. rectangular) shape. It wouldn't matter much to me if the value of the house was slightly lowered anyway, as I don't expect to move before I die.
I'm still considering the offer but I might well go with it. The price of (useful) building land around here (Suffolk) is probably about �200 per square metre, which would make the 'true' value of the piece of my garden as around �1500. However, the land isn't particularly useful to me, so selling at a third of the true value doesn't seem unreasonable. After all, if it was simply grazing land around here, it would only be worth around �25.
Thanks again for the replies,
Chris