This is not a thing at all.
You can setup auto pay by card or ACH but this is managed on the vendor side, not bank.
What the US uses is online bill pay which is a bank feature where you manage sending your money to pay the bill. If Monzo has a relationship with the vendor the payment is electronic, otherwise it will post a cheque.
You need to manually input the amount for the bill for variable rate bills.
Bank of America has a very innovative option where it will know the amount of variable rate bills which is amazing.
Auto pay is not hugely popular with many as people budget to pay when they can during the 30 day invoice period.