I think you are going to have your work cut out. I put in allotment statistics and found Leeds 96, North Tyneside 1,761.There doesnt seem to be one site with all the information. Happy searching.
I think you could start by contacting the local authorities of each area, they normally come under the umbrella with parks and cemetries. They take the revenue so they should have all the data. Good Luck Tbird+
http://www.nottinghamcity.gov.uk/sitemap/allot ments
this is nottinghamshire allotments, i put in google " nottinghamshire allotments " and that site came up, so i would think you'd have to put in all the counties name & ask the same question, got your work cut out there! good luck :-)