I’m not too sure how a card without a sort code, account number or name would work, would it just be a temporary card? Would you be able to invest in a card printing machine which can print a new card with the name and bank details on it? In that case, then I think a couple of ££ is a fair amount to pay for a next day delivery service and maybe £10 for the same day service, which I think is a little pricey, however I know it would be expensive for Monzo and I think it’s good to have the option in case I really needed a card the same day, for example, if I was going abroad in the morning. However, how much of London would you be able to cover, I’m in Essex but within the M25, would that still be covered?
I think that the dual card system that myself and some others have mentioned may be the better route to go down and cheaper for Monzo? I think it would also be a little more convenient as I know as soon as I get home after losing my card I have a spare one, all ready to go.