If referral was a once off explainable issue , you should have no problem.
If you do have an issue , explain what happened and then appeal it to card provider .
What a referral fee appears to show in your case, was you were not watching your account ,rather than a (hard) credit issue.
Its good you have perm public sector work , but that does not mean you necessarily pay your bills ! just that you should be a good mark for a credit card.
Have you a Debit Card from your Bank ? If not get one as it covers most things.