When you are changing from one provider to another, the "new" provider is responsible for the whole process and they will advise the "old" provider the date that take over is to take place. You do not need to do anything.
The only proviso to this is VM-O2 as they operate a different network.
You will pay a full month to your old provider , and any days paid for after the changeover takes place are refunded , if you pay by direct debit , leave the DD in place so any monies owed can be refunded by reverse DD.
As already stated , if moving between providers that both use Openreach copper network, then the gaining provider is responsible for everything, including serving notice to your old provider on your behalf that you are leaving them, you should know they have done things properly when you get a ‘sorry to see you leave’ communication from the old provider , if you never get this , I would check with the new provider that they have followed the correct procedure.