There are quite a few options:
- Click and collect online or pay for expedited delivery on a new phone by using Paypal (or similar) as it will take a few days to come out of your account.
- Borrow a trusted friends phone to install the Monzo app and transfer the money
- Borrow any phone, use a work phone, a payphone etc to call Monzo
- Email Monzo making sure it is very detailed to minimise back and forth but expect several days if not weeks
- Borrow some money of a friend, colleague, family member to buy a phone on the promise it will be immediately returned
That’s all I can think of off the top of my head but plenty of options there 
Personally I’d do #5