It was pointed out to me by e-mail that I should look at this thread, which is what I have just done.
At very little cost the first thing to do is to place a caution on the unregistered property with Land Registry, as was suggested by Arborlad a few postings earlier.
The details are on this web-site.
https://www.gov.uk/government/publicati ... gistration
Your need for a caution is because you claim that the unregistered land has moved its legal boundary during the last two years to include part of the land registered under your title.
Only be seeing the plan included with the conveyance when that property was sold to the current owner, will any court be able to decide where the legal boundary is located.
That is the only evidence that the brothers can furnish should this matter need to be decided by a court, but after reading this thread it seems as though there will be no clear evidence of what has happened to the boundary in the period from the date of that conveyance.
You think the father built a brick wall at the front and back of the house. That will need to be supported by statements of truth by anyone capable of confirming that fact.
The brick wall at the back was taken down and replaced with a wooden fence with a gate inserted into it two years ago.
That will need to be supported by statements of truth by anyone capable of confirming that fact.
The letter from the brothers' solicitor will need to be carefully considered in order to establish if there is a point of law that has merit in any claim being made.
If you want a personal opinion expressed on that matter then you will need to read the Private Message I will send you.
Before meeting with a solicitor that will incur legal costs, I am prepared to express an opinion based on years of experience dealing with land as a planning consultant and as a property developer, that will not cost you anything.
Registering a caution will ensure that anyone intending to buy the house next door will immediately be aware that there is a dispute about the boundary position. That is the first thing to be done.