It varies depending where you live and if it is fit for other uses e.g could you get PP to build on it or is it a future access to other areas which may increase the price considerably? A bit of garden that is of no use to anyone except the seller and buyer will not have a high price.
You can get the bit of garden valued or just decide what you want to charge between you. Check your deeds carefully for drain access, covenants etc and dont forget to see if the lost bit of garden devalues the price of your property in anyway? An estate agent will advise you for free on the value before and after you sell off some garden. The difference if any, in value is a good place to start negotiations. Dont forget you are doing them a favour so the deal should include all your costs and boundary changes such as fence moving change, to deeds etc. When I did this we had to get a release (not cheap) from 3 other neighbours first because with had an old long disused cesspit in the bit we sold off, so do check your deeds, its best to do this through a solicitor (buyer pays both sides).

This is good advice from Drc. I, too, would advise legal clearance. It can be much more complicated than it might appear, as I know from experience, especially if you or your neighbour wish to sell either house in later years.

I bought a section of my neighbour's garden two years ago. It was all done through solicitors so all the paperwork and any conditions are legally sorted.
For valuation, I suggest you check with one or two estate agents, try the Council (although mine washed their hands and wouldn't give me a figure) and another neighbour, who is an architect, gave me a useful guide figure as well.

What about Leasing it for a number of years like an allotment ?

Very messy when either want to sell Pimpernel?