The last ‘official’ position on this was when @tom was in front of the Treasury Select Committee, see below. Unfortunately, that was on 5th February 2019 and not much has happened to do with it since. I wouldn’t expect anything anytime soon.
Q192 Charlie Elphicke: Mr Blomfield, would you bother doing a deal with the Post Office, or do you just think, frankly, “We’re on the internet. We’re on the telephone. We do not need any kind of branch or physical presence”?
Tom Blomfield: We do not currently have a deal with the Post Office. We are in discussions and there is a possibility that we will, in particular for cash provision. The withdrawal or paying in of cash is declining, but it is not going anywhere in the near term. For the vast majority of other services, our customers prefer to use a mobile app, which is open 24 hours a day.
Q246 Chair: Does Monzo charge people who want to put cash in their account? Is there a charge for that?
Tom Blomfield: I apologise; yes, there is. We have two fees that I should mention, both related to cash. Cash is expensive. Depositing cash is a £1 fee using PayPoint. We are in talks with the Post Office and there will also be a small fee for using the Post Office. For withdrawing cash in another country above £200 a month, again because it is expensive, we charge a percentage fee.
Treasury Committee Oral evidence: Consumers’ access to financial services, HC 1642