Leaving inevitable exchange rate issues to one side for a minute…
What do we know, or can reasonably see happening to the provision of free EU ATM withdrawals from Monzo after a no-deal Brexit?
Are they dependant on any EU wide (cheap/free) banking licenses or deals for them to be economical for Monzo to provide?
More than likely as per free mobile roaming 
I wouldn’t worry though Brexit won’t happen if it did it would break up the Union and as Scotland would still be in the EU, we wouldn’t be subject to these charges, and ur all welcome when / if that happens
Riiiiiight… because the adults are in charge.
Forgive me for being a little sceptical it’s that obvious.
Would still be interested in anyones knowledge on what/if any legislations or 
banking deals underpin this offering from 
“Riiiiiight… because the adults are in charge”
they are in the Scottish government 
Well apparently as per EU site Monzo shouldn’t be charging for ATM withdrawals currently as we do not get charged for them here, that’s how I read it
This seems to describe a consumer benefit for being inside the . Which is the point of my nuclear brexit question…
Also, unless I’m reading it wrong, it’s also calling out special surcharges, levied on certain cards being illegal? I’m sure this would stay relevant afterwards. It makes it illegal to take these charges in EU as long as its a euros to euros transaction.
Given that Monzo provides the fee-free £200 allowance throughout the world (not just within the EU), I’d be surprised if there were any direct impact.
This rule is trying to prevent something slightly different: they don’t want companies applying different fees in different EU countries. Monzo applies their foreign currency ATM withdrawal fee structure equally across the EU.
“When you pay for something in the EU using your credit or debit card, traders and banks cannot charge you an extra fee – also known as “surcharging” – just for using a particular card. This rule applies to all card purchases (in shops and online) made within your home country or in another EU country.”
I think what the above is trying to get at, is that Merchants can’t charge you a surcharge simply because you are using a specific card (this is however dependant on whether you are in an EU country) - so for institutions like Monzo this may affect them as they are unlikely to go out and obtain a Banking Passport should a no-deal Brexit happen (I think).
As far as ATM fees goes I think @lumisota has put it right. I think you’ll still get charged the same over the £200 limit in say Spain as you would in New York.