Our allotments are unusual as they are all individually enclosed, so I know they are reasonably safe / clean from other animals getting in - although cats and foxes get into / over any fence or hedge. There may also be wild rabbits around with associated diseases that yours could pick up.
I have taken a rabbit down regularly as it was on the way back from the vet twice a week for his injections, and I used to pick up bunny forage on the way - he stayed in his carrier in the van most of the time, but did get the best freshly picked dandelions.
You would need a secure run (eg a folding metal one, or a big dog crate with no tray in it) with a fitted roof and some shelter from sun / rain, wind, etc. Something like a tarpaulin cover and a cat carrier would do - but would you want to carry the stuff there each time? Anything left on allotments tends to go missing...
Is your rabbit happy outside? Would you be able to watch it all the time? Is the ground fairly level so there would be no gaps under the run (dog crates have mesh on the base)? What would happen if bunny escaped? Does anyone take dogs there?
I'm not trying to put you off, but allotments are big places to loose a rabbit in and that would be heartbreaking.