How long before taking out a credit card?

Hello, we are hoping to complete this Wednesday coming. At the moment, my partner and I have a credit card each, his credit card has a limit of £3000 of which he owes £240, my credit card has a limit of £1200 and I owe £300. Both cards are not £0 interest anymore but we have been waiting to get the mortgage before taking out any type of credit.

When would you think it will be a good time to get a new credit card after getting the mortgage (the keys on Wednesday)?