OK so that's (unfortunately) your solicitor off the hook if you never advised them it was part of the deal (because you didn't know either).
To get the garage added to the LR land title that you hold you are going to have to demonstrate Adverse Possession for 12 years (I'm still assuming this piece of land is unregistered). To do that, you need to show 12 years of occupation and maintenance and since you've only just moved in, you can't do that.
One option is to wait until 12 years are up - then go for it. Only downside is if someone does hold an old deed for the site and turns up wanting their property back (unlikely I guess - the land is probably just owned by no-one). So you are unlikely to get shifted off the site.
The second option is more costly. You would have to go back to the seller and ask them to supply you with a sworn statement that they have had sole use of this garage for x years (as far as I know, LR will require a proper sworn statement). If the previous seller hasn't been there 12 years you would have to go back further to the previous owner and repeat the process. Armed with that information, you (or your solicitor) would be able to make an application for possessionary title. There is no reason why the seller would do this for you for nothing and the sworn statement will probably cost �50 or so to draw up.
The LR document to read, if you are so inclined is here.
http://www1.landregistry.gov.uk/assets/library /documents/lrpg005.pdf
But it is pretty heavy legal stuff.