No idea and it would be difficult to answer anyway because there are so many different employers. If it's a public park owned by the local council (and Greater London has 32 borough councils plus the City of London), the council will employ them. Some London parks are owned by national government so that's yet another employer. A privately owned garden - that's another employer. Syon House comes to mind - that's the London residence of the Duke of Northumberland, and you can look around the house and gardens. I thought of that one because like so many "stately homes", it has had to think of any way it can to raise money to keep the place going, and there is a garden centre there for your own horticultural shopping!
And as Guru Hank says, it is just about possible that who you see may be someone doing unpaid work as part of the community sentence they were sentenced to, though this is extremely unlikely as they wouldn't have the skills to do it right. Anyone sentenced to this is likely to be wearing a hi-viz jacket with "Community Payback" on the back. The kind of work you tend to get on a community sentence will be decorating (my former church got the church hall repainted for free this way) or clearing rubbish. A gardener needs to know what plants are and aren't weeds. The average young offender won't have a clue.
Another place to visit with lovely gardens, oddly enough, is a crematorium. Again these are generally run by the local council, or a group of local councils, and this will account for some employment of London gardeners as well. I just mention this because I happen to live in outer London not far from one, and with the local lack of cemeteries and space in church graveyards, most people who die locally end up there. At a crem there is obviously the chapel or chapels for funerals and the facilities for actually doing the cremations, but there will also be extensive gardens. I know this sounds a bit macabre but it's nice to walk around them.
If the family doesn't specify what they want done with the ashes (my family never does because we don't want to keep them or have any kind of memorial to visit, just remember our dead relative in our memories and photos - my late and very practical Dad would never have forgiven us for doing anything else, or spending his money on anything but the cheapest coffin "it'll only get burnt, won't it?"). the ashes will be scattered in the grounds. And out of respect for the dead whose remains are there, it is only right that the gardens should be meticulously kept, and they always are.
"London" does not employ anyone. It is a city.
Various local authorities, park authorities, companies and individuals employ gardeners. In total for Greater London, a good few hundred.
Generally the gardeners won't be employed by 'London' - they'll be employed by a park / parks, a private estate, a local council....
A number of them may be performing 'community service' as a result of committing 'community crimes'...
