Noise in flats can be a nightmare. The bloke upstairs complained with a rather rude letter pushed through the letterbox claiming the game I was playing on the PC was too loud.
Every saturday morning his missus plays music really loud when I guess he's out, wakes me up sometimes. I turn up the TV to drown it out.
Its not worth getting drawn into an argument. I've been there in the past in my old place and its a descent into hell. I've had major bust ups in the past and even one guy was violent and had to have the police called out on him on more than one occasion. I moved out in the end, living with a nutter downstairs was more stress than I need in my life. C'est la vie.
But to get back to the OP just saying "ignore the guy" isn't very helpful he probably isn't going to let it go, expect to receive letters from the council's Noise Abatement dept, they will take his word for it until it can be proved otherwise, expect visits from council officers armed with decibel readers, etc.