dispute with neighbours

[janham]

I share a roof and the neighbours agreed verbally to accept a quote they are now wanting another quote, the roof impacts my flat more than their property as theirs is below mine. the tradesman was given the go ahead and he has purchased supplies to fix the roof, where does this leave me legally?

A verbal agreement is legally binding as long as there is proof that they’ve accepted the quote. For example, any text messages referring to the work to be carried out or any witnesses that they’ve accepted the quote - you, for example. The fact that the tradesmen bought the materials is also strong indication that their quote had been accepted.
If the neighbours don’t want the work to be carried out, the tradesman could take legal action. Did he provide just you with the quote, or both neighbours? Do you share the freehold?

i would tell them it’s too late, they accepted the quote and the builder has been instructed and the work will go ahead

If they say they are not going to pay, and I would be insisting on the money upfront, then I would instruct the builder to do my half of the roof only

The other posters are correct. You have entered into a business agreement with your NDN. If they verbally accepted the quote and you subsequently instructed the tradesperson to go ahead then a contract has been formed. The tradesman has spent money on the basis of the agreement.

I would sent the neighbour a letter outlining your position and reiterating that if they cannot offer their written consent (make them sign a document) then you will instruct the tradesman to limit the work to your property only.

This is a totally different situation to that which often arises on Mumsnet. A agrees with B that B will get some quotes and then come back for A for discussion/decision. However B engages a workman without further discussion or agreement and expects A to pay half. A is under no obligation to pay for work to which they have not agreed.