On the whole, an individual can apply for adverse possession of land not actually owned by him or her if the requirements under the Land Registration Act 2002 are fulfilled.
Briefly, you must be able to show that for the period in question there was actual possession (known in law as factual possession) of the land without the owners permission or consent and that there was the necessary intention to possess the land. An application can be made at the Land Registry using form ADV1 (registered land) or FR1 (unregistered land).
Under the Act one must be able to show occupation of the land claimed for at least 10 years ending on the date of the application.
In calculating time one can count any time accrued by predecessors in title. This can be evidenced by a sworn statutory declaration from the predecessor.
Even if there has been an eviction from the land by the owner of the land or someone claiming under the registered proprietor it is still possible to make an application provided that the date of the eviction was not more than six months before the date of the application and that the eviction was not the result of a court order for possession.
Note that the application will be automatically rejected should the owner of the land object and issue a counter notice unless you have made reference to the three conditions in paragraph 5 of schedule 6 of the 2002 Act in your application.
If paragraph 5 of schedule 6 is relied upon then it is being asserted that it would be unconscionable not to be registered as the owner.
Alternatively, it is then being asserted that there is some other reason to be entitled to be registered as proprietor and/or that there has been adverse possession of land adjacent to your own for at least 10 years under the mistaken but reasonable belief that you were the owner of it, the exact line of the boundary with this adjacent land has not been determined under section 60 LRA 2002.
This is a complex area of the law and legal advice should be sought when making an application for adverse possession as there are many elements to comply with in order to succeed in an application for adverse possession.