Unfortunately you are unlikely to be able to use the law of adverse posession (the 12 yr thing) becuase you possibly have,to a sufficient extent [IANAL] recognised the “ownership” of the land by the care home, by offering to “buy it” off them.
To claim adverse possession (and Im bound to be wrong in parts here as it’s been over 15 years since my degree course) you need to do a few things such as:
Exclude others from the land (i.e. take “possession” of it, maybe with a gate or fence)
Make use of the land
Not “recognise” another party’s ownership of the land.
etc.
There’s probably a wiki on it.
If I were you, Id clear the land and use it, but do so with a clear distinction as to it’s boundaries so that a) if it’s taken back, it’s clear what’s what and b) if you sell the house it’s easy to explain and demonstrate the extent of your property title and how that bit is outside of it.
http://en.wikipedia.org/wiki/Adverse_possession
Adverse possession requires at a minimum five basic conditions being met to perfect the title of the disseisor. These are:
Actual possession of the property
Non-permissive, hostile or adverse use of the property
Open and notorious use of the property
Continuous use of the property
Exclusive use of the property