There's a difference between having an arranged overdraft, and being able to have a negative balance (also known as an unarranged overdraft).
Monzo's own help pages explicitly state that your balance can go into the negative, because offline debit card payments will not be rejected. They'll also gladly take you into the negative if you owe them money (e.g. through a Monzo Plus or Premium sub, or use their Flex service).
Search Monzo help for "Unarranged Overdrafts".
As far as I'm aware, there is no UK bank that will guarantee they will reject all payments and never let you go into a negative balance on a debit card transaction. This is also a profit centre for them, so there's little motivation to actually do so.
The mandated fee-cap introduced a few years ago has (or rather should have) curbed the view that overdraft fees are a cost centre. Banks are extremely proactive now, as soon as there is a hint you'll go in the red they'll ping you in a bunch of ways and remind you of what you can and cannot do; so I wouldn't exclude that some (or all) might now refuse to complete purchases when it would push you too deep into unarranged territory, because they cannot charge you more than a fixed amount, so it would become basically a free loan.
I'm with Barclays and Lloyds, and neither can go into negative(well, technically they can I suppose, but it's extremely hard to do. Any debit card or direct debit transaction will just get declined if it's about to go below 0).
I haven't lived in Europe for a while but it used to be common to issue online-only debit cards (VISA Electron, Maestro etc) for this reason, have these fallen out of fashion?
