If your landlord won’t negotiate, or you can’t agree a price, you can go via a more formal route so long as you have been registered as the owner of the property (with the Land Registry) for at least two years.
This involves hiring a qualified valuer to establish how much you should pay, and serving a legal notice on your landlord. If you still cannot agree you might have to go to a legal tribunal, which will make an order on your behalf.