A few years ago the pinguins took over (https://www.youtube.com/watch?v=x48eLs8tnJo) and basically every card in the UK is now either Visa/MasterCard/Amex and very few Maestro.
Ah. That explains why when my Maestro card expired, it was replaced with a Visa Debit card.
The latter is more widely accepted for online shopping (only some merchants accept Maestro, whereas everyone accepts Visa and Visa Debit usually works there), so I was happy.
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.
As far as I can tell, virtually all UK banks issue Visa Debit cards nowadays. Certainly Halifax, HSBC (First Direct), Natwest, Santander, Lloyds and RBS do which covers most of the population.
In the past a lot of cards were Switch, which became Maestro and then everyone dumped it for Visa.
Fortunately we still have the Link system where you're not charged for using an ATM that doesn't belong to your bank. cough Canada cough.
My British debit cards use either the Visa or Mastercard network.
My Danish one does too, though it also uses the local Dankort network if available.