If you switch via CASS (which you usually need to do in order to get any switching incentives), your new bank will automatically close the old one as part of the process – and also move direct debits, standing orders and salary payments across.
If you'd rather keep your old account open, or your old or new bank is one of the few not signed up to CASS, you'll need to use the older, slower and more complicated system. Your payments will still be switched over, but there's less protection if anything goes wrong and it's likely you won't get any of the switch incentives.