No. If you're not moving and switching supplier at your current address, your new provider lets your old one know.
Energy: your new supplier starts the switch and the industry switching process tells your current supplier, who sends you a final bill from the switch date.
Broadband: under Ofcom's One Touch Switch rules, your new provider arranges the switch, including between networks, and your old service ends on switch day.
Keep your old Direct Debit in place until the final bill from your old provider has been settled, then cancel it with your bank.