Hello, Kate, and thanks for that. It would be good if you could explain how your neighbours non-action affects you. For example, does the flaking paint affect your property or your access? Or would it de-value your house, assuming you own it, rather than rent?
I'm going to take a risk here, and tell of an episode that involved letting agents and landlord, rather than neighbours. The flat that my older daughter rented for 2 years, and left last year, was very prone to damp, which she started to notice just 6 months after she moved in. It was the basement flat of a converted Victorian house, and her letting agents (who should be banned forever from running such an enterprise!) did everything they could to pass the problem onto the agents responsible for the adjoining building. All the time, the damp got worse, my daughter's health was suffering, as were a lot of her possessions. Both the agents and the landlord refused point blank to do anything to help, so she went to the Environmental Health officer at the council, who did all he could to help, but he couldn't force the landlord to do anything as long as my daughter stayed. She was reluctant to go because (a) she'd have to pay out a lot to move to another agents and for a deposit etc, (b) she'd put a lot of work and money into improving the garden (c) she has an elderly cat, and there was nowhere else in her price range where there was a garden and would allow pets.
Eventually, the agents and landlord of next door realised that the damp was creeping through their building, too, did some research and found that poor 'cobbling together' of Victorian and modern pipes was causing water to leak and work its way up through the building. They had a massive amount of work done to put the matter right. At that point, my daughter found somewhere else and moved out, when the EHO immediately slapped an order (via the courts) on her ex landlord, banning him from re-letting the flat until the damp had been sorted. He was without a tenant in that flat for more than 6 months! No income for him, or the agents. Yay, a victory! 