cosysocks the very worrying part of this whole thing is when someone says this
"don't mind fence being there until it becomes damaged and needs replacing"
it means, that the vendors aren't push overs and won't relinquish the land, you on the other hand may just well not only give them the 20cm but more (they could be planning an extension and need that space) or they could dictate what type of fence they want and that could cost more.
Clearly the neighbour wanted the 20cm and you have to ask yourself why they don't want the vendors to move the fence. Why are they willing to wait? They hold all the cards, ie move the fence or we prevent your move.
Surely the pending sale of the house is the push the vendors need to satisfy the neighbours and then there is no dispute.
You are buying a house in a current boundary dispute. Please don't think that you can just go to court and have this all neatly resolved. Sadly it doesn't work that way. It also costs thousands and thousands of pounds.
Please have a look at the GardenLaw website, where people detail living in hell for years on end gardenlaw
Imagine the senario, you come home from work one day to discover a new fence has been erected not just the 20cm originally claimed but 60cm. How would you feel? Angry? You demand the fence is taken down. They say no, and if you touch it you would be guilty of criminal damage. You call the police, they tell you it is a civil matter to be dealt with by solicitors. Or you take matters into your own hands, remove the fence and wait for the backlash. How brazen are you?
I will point you in the direction of this very similar situation on gardenlaw neighbour moves fence