From a legal point of view, this is a very interesting area, where the law has evolved rapidly and is ripe for further development. The traditional position in Irish law held that is was a serious defamation to wrongly state or imply that a person's financial position was not secure. Any suggestion that a debt wasn't honoured or couldn't be honoured was particularly serious and would tend to attract large damages for loss of reputation. (It was said that the two most serious forms of libel were to defame a man's business reputation or a woman's moral reputation!) The Courts enthusiastically defended people's reputations and something like incorrectly refusing to honour a cheque and marking it "refer to drawer" would attract serious damages. This carried over into the era of credit reporting and (until recently) an incorrect report was also regarded as a serious act of defamation. In a 2001 case, a customer was awarded £10,000 against Woodchester Bank for such a report!
However, matters changed in 2015, when, in the case of Cornelius M. Cagney v. The Governor and Company of the Bank of Ireland, [2015] IEHC 288, the High Court held that such credit reports were entitled to benefit from a defence of qualified privilege (even if the information was incorrect) and thus refused to award damages for defamation.
So that closes off the defamation route. However, the GDPR route is potentially quite interesting. The bank holds and processes data and is obliged (among other things) to ensure that the data is correct. This is not a trivial responsibility and a failure can have serious consequences for the data subject. As the GDPR is a piece of EU legislation, compensation for any breach is supposed to be dissuasive in line with standard principles of EU law. This would suggest something more than mere nominal compensation. I'm not aware of any case where this has been tested but it can only be a matter of time.
In my opinion, the OP here has been done a serious detriment by the finance company. It is not simply good enough to talk of "gravy trains" or to suspect that there were "other reasons" for the refusal of credit. Even if that were so, having one's credit rating wrongfully damaged can have devastating consequences and it is only right and proper that there be an appropriate remedy in law with substantial damages.
OP would be well advised to consult a solicitor specialising in this area. Google throws up a few.