It's never easy to sort out this kind of thing, but the general experience on these forums of cancelling direct authorisations makes things far worse.
The reason for that is most providers provide any refunds due or agreed via that system. If you've cancelled the d/d then they can't, and the raising of manual credit payments by cheque or bank transfer seems to be more difficult than the Brexit negotiations.
In short - don't cancel!
Swapped from TT to TTB a few weeks back, not only did I get both of them charge me by direct debit for the same month, the rebate when I chased them up came by cheque.