Run the Monzo app, it will ask you for an email address
Enter the same email address you used to initially join Monzo - the app will then send a magic link to that email address
Using your phone’s email client to access your email (the same email used initially to sign up with Monzo), look for the very latest email from Monzo with a Magic Link and then follow the instructions in that email (it will have a box to tap on)
Once tapped on, the Monzo app will open and login to your account - and should work from this point unless you log out of the app
If the above does not work, please let me know where it fails.