The post office is tendering...
Bit of a no brainer really, and you wouldn't really want anyone else to do it. The Post Office has by far the greatest reach across the UK, and you could manage it in a single contract. No other organisation has this reach. I suspect that all of the hallowed 5 integrators would have suggested the Post Office, and politically it helps to preserve the network. You have to have biometric registration points within easy reach of all citizens, which counts out supermarket chains and banks, none of which have an even distribution, even within a region.
I suppose Public Libraries, Camelot and Pay Point are the only other organisations with a branch network that could cope, though here there's a substantial overlap with Post Offices.
BTW. The biometric enrolment process has to be monitored by humans to discourage fraud.