Can you get in touch with the people who owned the property before you did and see what their take on it is if you needed to - also check with the solicitor who obught to see what was said when you bought.
Any other occupiers, disputes etc. should have been disclosed and may provide more information about any arrangements in place say between the former owners and yourself.
Can you get a copy of any letting agreement that the guy on the garage says he is on?
If the guy is on a formal letting (albeit from a non-owner) then is he paying money to the neighbour to use your garage? If you can establish this and can successfully negate any claim of adverse possession I'd be interested in looking into this further.
Keep copies of all attempts you have made to get them out (I'd specifically state that he is in your private property without your consent) from as long ago as possible, send letters via recorded mail. If needs be a solicitor should be able to write a simple letter for you relatively cheaply.
Send everything by recorded mail so you have proof of sending and receipt. Trespass could be brought into it.
Could you threaten to change the locks by a certain reasonable time, giving him reasonable access to whatever is in there unless he signs another agreement with you formalising the terms of his occupation?
This is the Land Registry Practice Guide about claims for adverse possession...
http://www1.landregistry.gov.uk/assets/library /documents/lrpg004.pdf
Make sure all your details for contact are correct at the Land Registry so that if the Land Registry receive any application that they can contact you. This is very important!