How a leaseholder can buy part of a garden from the freeholder

Hello
I am a leaseholder of a first floor flat in a converted Victorian house. There are two other flats in the building - one below, one above - but they are both still owned by the freeholder so until he sells both flats (which I understand he has no plans to), I understand I cannot buy the freehold/share of freehold to my flat.
However, my query is.... the ground floor flat below me which the freeholder is renovating, has a huge garden and I have approached him about the possibility of splitting it and taking the top half for myself. It is physically possible and access to the top half would be via steps from my flat, to be added. He is very interested, but I would like to know what we have to do to make this legal:
- do I have to change the deeds of my lease and how do I go about doing that?
- do I have to go to the land registry?
- is there anything else I would have to get/change?
- how much roughly would I expect the legal/land registry costs to be?
- would I have to renegotiate the terms of my section of the land if the freehold was eventually up for grabs and would the other flats have access to/shared ownership of my section of land under a share of freehold regardless of my updated leasehold terms?
Any advise very much appreciated. Thank you!