They should have drafted a party wall agreement, and given you time to consider / refuse it well ahead of construction starting.
Contact that planning department of your local authority first. They may not have needed planning permission (if it's within permitted development), but planning can give you really good advice.
Buildings regs companies ("building control") are usually independent of the council, and you'll need to pay them to come out. They should be able to do a structural survey and a report, and ideally those costs will be passed on to your neighbour, along with any costs to repair any damage. If building control can't do the structural survey, find a reputable independent structural engineer.
In writing, request that your neighbour cease all works until the survey is complete. They may or may not comply, but if they continue and further damage is caused it will make it easier for you to claim damages.
As pp said, document everything: all communications going forward with the neighbour, and photos. Plus, in a letter or email, write down and send to your neighbour exactly what happened, with dates and photos, so that you have a joint record of what's happened to date. Include "we requested that all works cease on XX date, while we undertake a structural survey".
Take photos and document the state of walls/ceilings on the floor below, so that if there is structural damage and it starts to effect that floor (eg cracks or damp appears), you can prove it happened after your attic was damaged.
Do not engage with the builder. They may get nasty if works stop. If they were "good" builders they would have done this by the book; the fact that they haven't tells you all you need to know. Grey rock them (don't speak to them, nor take calls/messages), and record any interactions on your phone. Likewise with your neighbours: no matter how nice they've been to date - they won't be so nice if they have to pay to make good.
Remember: this is not your fault, and by taking the steps above you are not being unreasonable. Stay calm, get expert and independent advice, and document everything - and this will get sorted. I've been there, and it all worked out fine in the end!