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Didn't apply for credit card but got an application denied letter?
Do you have any ties to your old address? In particular are you the LANDLORD? This could have been a precursor application to test identity evidence and setup a mortgage. The perps may even have legally changed their name to yours and even be living in, or close to the house if it is a share house to intercept this kind of mail.  Otherwise someone's database may have been breached, so it is important you try to work out where this information used in the application came from. If they are an illegal you may be racking up Council Tax somewhere or end up paying income tax on their earnings. In any case your character has probably now been damaged. So do follow it up right smartly.