It depends on the supplier. Some will take your first payment at least 10 days after your switch is completed. Others will take payment immediately – in which case you may end up paying your final bill with your old supplier and your first Direct Debit with your new supplier in the same month.
This isn't money you'll lose – it goes into your account as credit to pay for your future energy use, and if you build up lots of credit you can always ask for it back, or you'll be refunded when you switch again.
If your last payment to your old supplier put you (more) in credit, you should get your credit refunded once the switch has settled and your old supplier has determined your final bill.
Generally they try and pay this to your bank account, so it's worth waiting to cancel your Direct Debit (if that's how you pay) until you've received this credit. If you owe your old supplier, it'll be in touch about getting you to pay your final bill (or it'll take it via Direct Debit - provided you haven't cancelled it in the meantime).