Howdy. Welcome to the Vine.
I am also in Blaby District but at the other end to you.
I'm looking on google earth over Sapcote and there appears to be some allotments off Bassett Lane... have you seen those..?
Also there appears to be a small Allotment looking site off Leicester Road next to a field (leicester Road from Coventry Road), big drop of water accross the field...is that an allotment..?
Also another one off Grace road.. Spring Gardens it says..
You might be better off visiting these sites and looking for contact details on the gate, at the very least there should be contact info there.
Have you tried Leicester County Council..?
Allotments Leicestershire Villages - Broughton Astley - Find My Nearest Also try this, click on to the blue tags.