Can they sell their house?

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Next door neighbours have built a decking and wall which overlaps our side of the property line by about ten cm.
We have asked and written to them to alter this so it does not impede our property. We have asked a lawyer to write to them to request alterations.
Nothing.
We are seeking legal action through our home insurance. They are slow to procede.

Looks like neighbours will be trying to sell their house. Can this be go ahead with a dispute going on, and what action is available to use? We are in Scotland if relevant.

not a legal eagle nor scottish but I do have a suggestion. Look into "lodging an application" on the land registry. This would show up when legal searches are made during the sale process and would flag to the potential buyers that there is an issue. You might want to get the information on doing this and inform your neighbour that you plan to do it....might be the kick up the bum that is needed. BUT (huge but) boundary lines are rarely if ever accurate to 10cm (4 inches) Unless you have got recent surveyor proof, you may be on a hiding to nothing....useful website though https://www.boundary-problems.co.uk/boundary-problems/myth-bust.html

Contact council planning dept

In England & Wales, you legally have to disclose any neighbourhood disputes as part of the sales process. And if you’re known to have misled the buyer they can take you to court over it. There’s some expensive examples of case law where things weren’t disclosed & bit the seller on the arse. Given Scotlands whole process is a lot more efficient, I can’t see how they’d be able to sell without disclosing the dispute, especially if you have dated letters and proof of postage.

has there actually been a dispute though?

Technically yes. Because they have complained about their decking (in written form), and are seeking legal representation due to lack of response. Albeit early stages.

But if they do not disclose the sale will proceed

Yes, if they’re willing to lie on a legal document. But that’s a dangerous game to play.

Do you want them to sell? If not, a big banner in the garden saying ‘we’re in legal dispute about a boundary’ would make everyone run a mile. IANAL, obviously.