Could you give me some advice on the most efficient way to purchase the freehold of my house?
Does the freeholder wish to sell? You should ask them (or preferably ask your solicitor to ask them), since it will save you a lot of trouble and expense if they offer you the freehold at a reasonable price. You could then ask the solicitor to complete the conveyance for you and register the new arrangement at the Land Registry. You have a legal right to purchase your freehold under the Leasehold Reform Act 1967, but forcing the freeholder to sell and establishing the true value of the freehold is a complicated and expensive business. It would probably only be worth it if your lease was due to expire in the near future or your lease contains inconvenient restrictions.