Hi, I have lived in my rented house with my small daughter

Hi,
I have lived in my rented house with my small daughter for just over a year and a half. Since moving in my neighbour (I live in the centre of a terrace of houses) has written me numerous letters regarding noise. This was initially pertaining to my boiler which is at the back of the house and he has asked that I not use this in between the hours of 10pm and 8am as it was affecting their sleep, which in the middle of winter in a house with single glazing to the back and a small child is not always feasible.
Since then the letters have become more accusatory stating that I have a radio on at night (which I don't), that I am skyping people at 3 in the morning (which I am also not as tend to be fast asleep well before then) from my daughters bedroom.
I have asked my other adjoining neighbour if she has any issues with noise emanating from my house and she has stated that she doesn't hear a thing and is a light sleeper as she has two children.
Unfortunately he appears to be escalating and has had a number of issues with all of our row of neighbours (complained aggressively about children playing ball games 2 doors down, complained that 1 neighbour had used our shared access at the back too many times, complained that another neighbour was singing in the shower, etc.). Unfortunately his behaviour appears to be escalating into aggressive and unreasonable behaviour to the point that a neighbour last week had to call the police after an aggressive and abusive tirade about treading too loudly on a drain in our shared access outside his house.
I have had another letter today claiming that the sound of a radio from my daughters bedroom has kept them awake between the hours of 00:10 and 02:10 for the past few months and that there are thuds coming from my living room.
I work full time and my daughter is at school so our house is empty for most of the day only returning at 6; however not wanting to upset or cause any aggravation with neighbours I have now moved my 4 year old daughter into my bedroom as the majority of complaints emanate about her bedroom. I have also refrained from using my heating and hot water systems; but this doesn't seem to have alleviated any of his issues.
I don't want to move as both my daughter and I love our house and our other neighbours but I am starting to feel harassed and intimidated by my neighbour and my child is visibly frightened of him, having heard some of his arguments with other neighbours.
Is there anything that I can do?