I'm not sure where the parent poster lives, but I've read about this system (called allotments) in kids' fiction; it was apparently common in the UK (and may still be). Some of the characters in the stories used to be growing vegetables in their allotments :) It's something like small plots of land in or near the edges of towns, so easy for the renters (town-dwellers) to reach after/before work or on weekends.
I've done a good amount of gardening myself, and it is great fun (apart from being a good way to get fresh vegetables etc.)
Yes,it's a UK tradition which, if I'm correct relates back to WW2 and growing your own stuff in harsh times. It's still really common in the UK and one can get a good plot of land (within London boundaries, maybe about 100 sq mt) for less than GBP100 per year, often within 1 or 2 miles from your house. It's a fantastic deal.
I've done a good amount of gardening myself, and it is great fun (apart from being a good way to get fresh vegetables etc.)