In Brazil, you can enable the same card you use to manage your bank account and withdraw cash as a Visa/Mastercard credit card. So every time you make a purchase you get a prompt like this
1. CREDITO
2. DEBITO
where you choose if you want to pay with credit or debit.
Last year I went to the UK on vacation. While paying my bills I noticed most people wouldn't know what to do when prompted. They would look confused and just hand me the card machine and let me handle it.
When I use my card outside the UK in a country where this is the norm (e.g. Italy) I am asked to choose the 'circuit' before paying, but the only choice I am given is "VISA DEBIT" - this is on ATMs and Chip&PIN machines.
I don't think any UK banks have their own payment network. The cards you get to access the account directly are debit cards (usually Visa Debit or Maestro), some (i.e. children accounts) give you a 'cash card' which only works at that bank's ATMs.
This never happens in the UK. It confuses the heck out of me in countries where it does (e.g. New Zealand).