Hi Dartmouth - same thing happened in our road sometime back in the 90s (although in this instance we are the beneficiaries of a slightly larger garden as a result) and the old lane doesn't show on any maps so may be a different scenario.
As I understand it, the rationale for owners of houses on our street "acquiring" the land in the lane was because they had historically been the bin alleys but bins were no longer collected from the lanes so it was "dead" land if you like. Added to that was a spate of burglaries in the street where access was gained via the bin alleys.
A number of home owners in our street therefore extended the gardens so that garden backed onto garden of the parallel street rather than the gardens backing onto an alley.
Subject to when all this happened in your street, it is likely that whoever has fenced off the access has gained ownership by what is known as adverse possession (what is sometimes called Squatter's rights in lay terms). I wouldn't advise ripping down the fence as, even in its dilapidated state, your neighbour may have acquired legal title to the land and you'd be opening yourself up to the possibility of a criminal damage claim!
I also think it'sunlikely that it's a public right of way and if there ever was a right of way, it has probably been extinguished by now (again, subject to when the fence was erected)
Have you spoken to the owners? It might be worth having a chat with them to sort out the repairs to the fence (I am obviosuly working on the assumption that they are reasonable people but accept that's never a given!)