1. There are two issues here which need to be dealt with. Firstly, there is the issue of ownership of the land. Here you have a right to ownership of the law by means of the doctrine of estoppel by convention. This basically postulates that if all parties, such as your selves and your grandmother and these people who are her successors in title, act on the basis of assumed facts about ownership, they will not then be allowed to resile or go back on the facts as agreed by everybody. This means that you will obtain title to this strip of land by virtue of the doctrine of estoppel by convention. These successors in title will not be allowed to claim ownership of the land after 60 years as all parties up until this date have acted on the basis that your parents owned this strip of land.
2. Secondly, there is the issue of the current situation whereby your parents have been ejected and forcibly removed from the land. Here you need to go to your local County Court with the aid of a solicitor and get an injunction preventing and restraining the other parties from forcing you off the land until a determination has been made by the court about the ownership and correcting the Land Registry ownership as it currently stands. So you need to hire a solicitor and barrister and claim damages for the wrongful behaviour of your neighbour and the men they employed to chuck you off the land forcibly. As part of these injunction proceedings you need to claim relief by estoppel by convention and seek the rectification of the Land Registry title so that ownership now vests in your parents.
3. Ultimately, your parents need to go to court to get ownership of this strip. So the sooner you see a solicitor and get proceedings in being, the better.