I’ll try to clarify further below:

• customer does not pay the fee, as stated above. The cardholder’s **bank** will pay the fee (unless you are using a cash machine actually operated by the cardholder’s bank)
• high street banks generally only operate the ones attached the their branches, although there are a few exceptions.
• the vast majority you see eg in the wall outside a petrol station, a Tesco express etc, these will be operated by a third party.

Here is a link showing data from 2019 that’s shows just over half of all machines are operated by third parties, collectively the banks operate under half.

A point to note, if a Nationwide cardholder use a Halifax operated cash machine, the charge is still happening (again, not seen by the customer trying to be really clear on this). So it’s not to do with third parties but about paying for the infrastructure for banks to talk to each other. The charge relates to LINK which is the system keeping them all talking to each other - again not being rude but this is something that I wrote above.

I only responded to you originally because I thought you had some information that the banks run most of the machines, which piqued my interest.