After reinstalling the app I am not able to log in. I tap on “Sign In”, I enter my email, I receive and email with the link to log in, but when I tap on it I land on a page where I am asked to transfer £100 to receive a new card.
I already have a card and I would like to access its balance again…
assuming you cant get in app chat for support - try emailing - help@getmondo.co.uk - and they will sort it out for you
This means that you’ve logged in with a different email address to the one on your account.
Mine is slightly different, I get the link and when I go on the link the app re-opens but asks me to enter the email address. Pretty much a never ending loop! 
Can you try deleting the app, deleting all of the login emails you have from us and then starting again? Thanks!
If this is iOS then there’s also Settings > Monzo > Reset Session
This was used to fix a problem I had.
Just a quick heads up - one of the Monzo developers has just told me that logging out & back in again resets more settings, than resetting the session so it’s generally the better option.