Welcome to the site.
Your starting point is section 23 of the Small Holdings and Allotments Act 1908, which essentially says that if the council (whichever one it is) is of the opinion that there is a demand for allotments in its area, it shall provide a sufficient number of them. The duty to consider this is triggered by a representation in writing to the council from 6 registered parliamentary electors or council tax payers that there is a demand for allotments.
So you first need to get organised and get at least six of you to write to the council of the geographical area in which you live. By citing the relevant legislation, then at least it shows them you mean business.
If there already are allotments in the area and they don't have a waiting list, you may be onto a hiding to nothing. Even if there aren't, then you still may not be successful as councils have historically been reluctant to take action.