My experience of changing the type of account I held with a bank suggests that it's not necessarily that straightforward.
For example, I wanted to change a Santander account from one that only provided a 'cash card' (for use in ATMs but not in shops), to one that provided a proper debit card. I called in at my local branch, taking ID with me, in the hope of doing it instantly. I was told though that I'd have to make an appointment to see an adviser in a few days time, in order to set up a completely new account. That appointment lasted nearly an hour, with countless bits of form-filling and computer checks on my credit status (even though I wasn't seeking an account that offered overdraft facilities). I was then told that I'd have to wait about a fortnight for a decision from Santander's head office!
So don't expect instant success!