Schmungo
You have received some good advice on the other thread, and you are using a solicitor.
It is surely extremely probably that this has been raised now precisely BECAUSE you are proposing to move, and these petty neighbours realised that it is their best opportunity to get what they want because:
1) It automatically creates a 'dispute' that you would have to disclose to potential buyers, who may therefore be put off
2) They consider the best chance is for you to agree to moving the boundary now as you have less interest in maintaining the status quo on the boundaries - just getting sold and moving on (at least that is probably their perception).
The other correspondents talked about 2 potential legal mechanisms by which the land is yours:
1) The Prescription Act 1832
2) Adverse Possession
Whilst I am not saying thin & cripsy is wrong (I, too, am only an amateur in this), I had always believed that the Prescription Act applies to rights of one landowner over another's land (NOT to ownership of that land). It's most common application involves a right of access, it can also apply to a right to light, and there are various other rights it can be used for. The period of time is 20 years minimum, as others have pointed out.
Adverse Possession (known as Squatters Rights in the popular press) involves occupation and maintenance of another's land - leading to the eventual opportunity to register the land with the Land Registry as one's own. I am not clear why one of the correspondents says you should not be using Adverse Possession - because to me it is absolutely the legal mechanism that should be considered. Except that in the case of 2 inches of land, the argument goes back to 'where the fence exactly is and how long has it been there'.