The Builder is to blame.
They have been negligent and you don’t need to have had a contractual relationship with the Builder in order to pursue them – they owed you a Duty of Care (working beside/on your property), the damage was entirely foreseeable (you warned them on several occasions) and they have clearly breached that Duty of Care and directly caused damage to your property.
But your Neighbour (if the decent, supportive type) should be using their existing relationship to lean on the Builder to make good the damage.
It depends upon a few factors, but on balance it’s unlikely the Neighbour will be classed as the Builder’s Employer – more likely the Builder is a Bona-Fide outfit.
The Builder should have Public Liability Insurance to meet claims arising from Damage caused to Third Party Property. Their own Excess level should start in the region of £500-£1,000. Of course, Public Liability Insurance is not legally mandatory, so they may not have it. Regardless, it doesn’t change or remove your right to pursue them to make good the damage from their own pockets.
As mentioned, any records, documents, photos etc. you have will support your case.
Ideally, the Builder would do the right thing and fix the damage, but if not, then you’re into a longer, harder battle.
In that event, the simplest way to deal with this is to contact your own Home Insurer now.
Firstly, see if they will accept the claim as Accidental Damage, or similar (if you carry that Peril). If they do, then they can pay to fix matters. Then, it’s for your Insurer – and their well-oiled legal machine – to Subrogate against the Builder, who is ultimately to blame, and sue them on your behalf to recoup their claims outlay. If full recovery is made from the Builder – which will take a long time – then the claim will amount to very little, if anything, on your Home Insurance claims record, and will not overly count against you. This gets your property fixed the quickest and leaves the nasty, drawn-out stuff to your Insurer. You may have additional Uninsured Losses e.g. your Policy Excess, which the Builder still remains liable for.
In addition, your Home Insurance Policy may come with a Legal Expenses extension as an extra (which you may have had to opt-in & pay for), which may meet the costs (up to circa £50,000 typically) of pursuing legal recourse against the Builder. If so, there will be a free 24/7 Legal Advice Helpline you can call to discuss initially. Cover is likely to be subject to a ‘reasonable prospects of success’ caveat, but it sounds like it’s pretty clear cut in this instance.
This Guardian article explains it a bit:
https://www.theguardian.com/money/20...consumerissues