Hello Rachel - as you state the Notice on the register is of the claimed right and our PG 52 explains this in greater detail
Easements claimed by prescription (PG52) - GOV.UK (www.gov.uk)
We can't advise you on the legal implications and you should rely on your own legal rep in that regard and if the claimed right is deemed insufficient discuss options such as obtaining a deed of grant from the registered owner of the land over which the right of way has bene claimed