Your neighbour will rightly look to be compensated for any damage to property so you need to ensure cover is in place. You should insist on a copy of your builders employers and public liability, contaractors all risks(if they have it) details, this can be just a letter from broker noting insurer, policy number, period and limits for your own safety. you shouls also specifically ask will the cover extend to cover neighbours property (get response from insurer or broker)- under the builder public liability policy it should. However it wont cover damage to grass by the scaffolding or access to it so best to come to agreement with neightbour before work commeces - garden centre voucher, few bottles of wine......
You need to inform your insurer of the work taking place, they may reduce cover to fire only, try to get them to maintain full cover but you might have to lock any valuables in a room which cannot be accessed from the "open" sections of the house or move to another premises....... It is unlikely that any insurer other than "current" household insurer will cover this activity, fyi they will ask about security etc