Sorry about your situation, I do have sympathy with it and can see how difficult it would be especially if Monzo is your only/primary bank.
I would suggest getting in touch with Monzo via email at help@monzo.com or phone 0800 802 1281 to see if there is a process you can use to verify yourself and get things activated manually.
Otherwise, you will probably have to borrow a phone from a friend or family member, as others have suggested.
Failing all of that, it looks like your only solution is to buy a new phone or switch to a high street bank (unfortunately).
Let us know how you get on!