'Good' credit rating, cannot get a credit card

Dr_Cuckoo3

The OP mentions that Santander is his bank of more than 10 years

Assuming that the account is a current account and is still open then the simplest method of obtaining a credit card is via pre-approval and this does not require a credit reference search (although Santander are aware of some of the account holder's credit reference data without a search)

Another indication of the Bank's opinion of the customer is the behavior score and you may wish to ask branch staff for this (650 - 700 in my case over the last few months)