In reply to Queenie:
> Are you friendly with other allotment people?
A few of them, but no-one's really around at the moment and haven't all got sheds.
> If locking up your shed is a concern, can you make a discreet hole so they can gain access when it's closed, just for the duration?
The shed windows are ill-fitting plastic, I assume the birds got in that way and could get out again, or there might be a gap in the eaves. I haven't been there in months so they didn't get in the door.