The fence in my back garden blew down in recent gales and my next door neighbour says that as the posts are on my side of the fence, it is my responsibility to pay for it to be replaced. Is this true?

Not necessarily. Many years ago, title deeds to properties gave no indication as to the ownership of boundary walls and fences. However, it gradually became more usual for ownership of boundaries to be allocated within the title deeds and indeed, over the last 30-40 years, virtually all properties built will also mention ownership of boundaries. First of all, have a look at your title deeds to see if the fence is actually yours.