I bought some garden off a neighbour and all the above are helpful points. We used a RICS valuer, who guesstimated the impact on the value of both properties to come up with a suggested value. Mine was positive. neighbour was negligible. In our case the neighbour wanted a covenant that it would remain as garden so I didn't flip it to a developer. I was quite happy with that, but wanted a defined period of 25 years otherwise these things are a PITA later on.
In my case the neighbour had no mortgage so I bought the new land on a separate title - at some point I can merge with my main title. I didn't want to deal with my mortgage company unnecessarily because I was in a long fixed term, and the land could be sold separately if I need to get some money at some point.
At the end of the day the value is what you two agree. Your case is interesting because it is a swap of land so the delta value may be low - but beware of transfer values and any tax implications which will be on the land value, not the delta.
Do consider covenants if there is any possibility of the neighbour using the new land to develop.
Get a conveyancer who knows what they are doing. I wouldn't recommend mine or my neighbours! The covenant took a year to agree the wording, I did most of the work.
Parking can add a fair bit of value to a house in London. Garden land value kind of depends on the impact on what is there. If no, or small garden, then adding garden is pretty valuable. If there is already a large garden then trimming or extending a bit doesn't usually make much difference to the value of the house.
BUT it might be worth more to you that the 'book' price. We were like this. A larger garden might mean you don't need to move - so save all those costs and hassle.
As a comparative value for you:
6 years ago I paid £15k for a 75 sq metre plot. London zone 2/3 border, miles from public transport. With a covenant to keep as garden. It doubled the size of my garden and has been fantastic during this lockdown!
We both paid our own legal fees (neighbour was lovely), I think they even paid for the valuation.