It doesn't matter what sort of mortgage you have. However, many mortgage companies demand a final payment once your mortgage falls below a set amount, as it costs too much to administer.
I'm surprised your mortgage company still have your deeds - many don't hold on to them as they have been superseded by the Registered Title at the Land Registry.
If you have such a small mortgage the lender will not allow you to go on to a fixed rate at the end of the current agreement, and indeed may close the mortgage altogether, asking you for your final payment.