Why Are We Back To Square One?

The BBC has issued yet another word appeal:

"Wanted: Printed evidence before 1960; information of the word's origin.

Can you help the OED find out once and for all why we say 'back to square one'? Some say it's to do with radio football commentary in the 1920s and 30s (there are commentators' grids in which a section of the pitch is labelled 'one'). So if this is the case, it is very curious that the expression isn't documented until 1960. Or does it come from board games like Snakes and Ladders? Do you have an old game which includes the instructions to go 'back to square one' from earlier?"

You can find the current OED entry here, and contact the BBC’s word sleuths here.