I assume you want to include the path in your garden and prevent neighbours from coming across it. As it is on your deeds as a shared path it is very likely also on your neighbours deeds in the same way. You can check this by getting a copy of their deeds from the land registry online service for a few �s.
If it is on their deeds, you could only claim it or buy it (assuming you can find out who owns it - which may be possible from land registry, but it might not be registered if last sold many years ago) if your neighbours agree and it is then deleted from their deeds.