I agree with boxtops, you must be noisy, or at least must have been noisy for a complaint to have started - or is there more to this than you are telling us?
If they can see what room you are in get some net curtains
If they can hear your TV, get one of those things that you can use headphones to listen to with
Get your hearing checked out
Not sure washing a rug at 8 pm is a nuisance but was the dog out there with you barking?
Start your own diary about them and their antics
You do not have to prove your innocence at all but your neighbour could be successful in their anti social behaviour gripe against you with no evidence whatsoever
You have been spoken to by the council, personally I would take note, make sure I am complying and take strides to stop it happening again
Get a peephole for your door as well and dont open it to them
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