Admittedly it does push the limit problem in the wrong direction…
However as others have suggested, if OP is going to hit Monzo limits his best option is to open another account, even if just to transfer money to Monzo. I’m just suggesting he include the cost of depositing the cash (bank’s charge, and perhaps your time+mileage to find a still open branch/post office). Starling business would be perfect for this.