Adverse Possession is just a name given to the legal process of someone claiming ownership of somebody else's land. Of itself it is not a holding of the land like freehold, leasehold, licence etc. It is only a legal process that could just as well be called Mrs Bloggs Currant Cake for all it matters. In your specific case for a long period of time you have unlawfully occupied a portion of another's land that has a boundary contiguous with your own. You have been told to withdraw. Your only defence for not withdrawing is to claim that under Mrs Bloggs Currant Cake it is you that is now entitled to the freehold, not the original owner. Claiming you are now the freeholder is your only defence, there is no other, and in pressing forward with this you are notionally moving the contiguous boundary to around the contested area and merging the contested area with your existing garden, that is why it is a boundary dispute. For your defence, you will be required to prove that under the rules for Adverse Possession (which were first written down over 900 years ago with much case law since) that you have become the true freeholder. It obviously will be contested and preparing a matter like this for trial requires expertise and is complicated, protracted, outrageously expensive and will blight your property. You do not in fact stand much chance of success:
(1) if you had erected part of a house, factory or other permanent building on the area you would stand a 95% chance
(2) if you had erected a shed, greenhouse or similar on the area you would stand not more than a 50% chance
(3) if all that you have on the area is a cauliflower, two tulips and some mowed grass you stand no chance.