When you leave a contract with any supplier, they will use your final meter reading to calculate how much energy you used in your time with them, and share what is owed with you in a final bill. This will be either a refund (if you've overpaid and have built up credit), or a final charge (if you've used energy that you've yet to pay for).
As this final bill can come up to 6 weeks after your switch has completed, you may find that you're paying both suppliers in the same month, which may feel like "double billing", but is actually just the settling of balances.
The first payment due to the new supplier often comes before they have even started supplying you with energy. This "buffer payment" or advanced payment, is what allows smaller suppliers to undercut their larger competitors. Whilst this payment doesn’t pay for energy immediately, it will be held on the account as credit and will be refunded when switching away, if not used beforehand. You will always be able to see what your current balance is with suppliers, either through your online account, or through a monthly statement/bill that they send to you. If a large credit builds up, and you stay with the supplier, you might be issued a refund or a reduced Direct Debit amount, both of which you can request yourself.