Thanks for your answer.
I didn't realise I could do that without first closing the account with the current supplier. I will certainly try that if it's possible.
Regarding the bill that will (eventually) land on our doorstep for the last 8 months...
The current supplier is one of the most expensive, and we probably could have made savings of several hundred pounds if we'd switched straight away (which I didn't think we could do without closing the account first). Would I be right to ask them to reduce the bill by that amount to match the cheapest supplier?