As I'm a very new forum member, I'm coming late to this thread. Some good advice already given IMHO. However, I would suggest that, if you have wholly paid for the new gate/s, you send a letter to your neighbour (over whose land you have some access rights) explaining your choice of action: in other words, while you might have chosen to pay for gate repairs this time round, this should not be construed as meaning that you will wholly pay for any/all future costs on maintaining your common boundary.
I don't condone his/her position by any means, but I don't doubt there will be an irk at paying towards maintaining access to one's land to benefit someone else. HOWEVER, maintaining hedges/fences between your properties is more obviously to mutual benefit so I suggest you make some sort of statement to make sure you are not establishing some sort of precedent. (Obviously I do not know what your Deeds say, but one cannot be too careful wrt easements. In my experience, solicitors think no further than standard clauses for Deeds of Grant etc and really do not consider the psychology involved: servient property owners will, everytime, feel aggrieved when a bill comes their way for services that serve the dominant property more than them!)
