It is tiresome, we have been lobbying the council for years to extend our site because of our waiting list. Yet we have plots, those people on the waiting list are not keen to do the job for themselves, even with our support.
There is a law. The small holdings and allotments act which you can find on line.
A friend of mine got a group of 6 together in her area and found some unused land belonging to the council, she contacted the county councillor with the portfolio for allotments and eventually, she was allowed to have the land for one year, they made their own constitution and registered it at the council and then got a grant to develop it. After the year (I think they were checking to make sure it was used) she got a three year lease which is renewed every three years.
It took her about two years altogether from getting the 6 Interested people, finding the land, to get digging started on the plots.