Eh banning cash wouldn't stop the criminal element - they'd just shift to using transaction methods that allow for more anonymous payment methods. Heck they could simply open and close accounts under false details if needed and transfer the money around. Heck do it enough times and you make a massive papertrail to bog down the police.
Personally I think the main drive to stopping cash would be so that everyones money has to be tied up in the banks or in investments. Keeping the banks from being closed down and also preventing a rush on the banks should they have any future accidents. Since you can't demand your money if there isn't any
But honestly money as cash is still widely in use; even though I hardly use the stuff myself I'd hate to be left in a situation without it. £20 in the pocket lets me pay cabby or train fair (well provided I only want to go one stop away -- shakes paw at rail prices!) or heck any market stall.