The governing legislation is the Small Holdings and Allotments Act 1908 and the wording is:
(1) If the council of any borough, urban district, or parish are of opinion that there is a demand for allotments in the borough, urban district, or parish, the council shall provide a sufficient number of allotments, and shall let such allotments to persons resident in the borough, district, or parish, and desiring to take the same.
(2) On a representation in writing to the council of any borough, urban district, or parish, by any six registered parliamentary electors or persons who are liable to pay an amount in respect of council tax resident in the borough, urban district, or parish, that the circumstances of the borough, urban district, or parish are such that it is the duty of the council to take proceedings under this Part of this Act therein, the council shall take such representation into consideration.
It's a minefield. The best source of help is the National Society of Allotment and Leisure Gardeners who can help you fight to get allotments established.
http://www.nsalg.org.uk