On the matter of fraud, credit scores etc I would strongly suggest doing something about this! I know you are probably a long way from even thinking about buying a house, but firstly your credit report is important for banks, credit cards, mobile phone contracts and many other things too. And secondly when you do need a mortage, you want a credit report that’s squeeky clean over the last several years! (I think fraud is meant to be struck from your report after 5 years, but I’m not too sure about this.)
With that in mind, here are a few thoughts:
Firstly: If someone else commited fraud (whether with your card or not) this really really shouldn’t matter in your credit report. It was someone else, after all!
Secondly: Have you actually checked your credit report, to see if it actually suffered as a result of this? (The full report is much more important than the credit score itself!) There are various ways of doing this, but you have a statutory right to see your report (i.e. by law the reporting agency MUST provide you with your report if requested). However, they may charge you, and there are free ways of checking your credit report
Thirdly: Maybe you’ll find out your credit report is unaffected from this. In that case: 
If not: Address the issues. As @anon4562461 mentioned, the first point of reference is the bank that made the report. Get them to withdraw it. If they really refuse (but don’t give up too early!) consider posting a notice of correction which you are fully entitled to do (although some say this may be counter productive, so try the first route first, and research a little before actually doing this). Read more here: Unfair default or other error on your file? You need to fight it
Fourthly: Work on re-building / improving your credit record. One of the best ways of doing this is getting a credit card, and using it right. (See the link below for loads of tips, and to make sure you are not using it wrongly, because as much as a credit card can boost your credit score if used correctly, it can ruin it, if used incorrectly)
Finally, I would thoroughly recommend reading this one in full - It’s long but VERY MUCH worth a read in its entirety:
Finally finally: A personal story to motivate you:
About 2 years ago I never thought I would ever buy a house. However, I got somewhat obsessed with my credit report after a friend had his ruined through fraud, and managed to rebuild it within a year. So, I signed up for the various free credit reporting sites mentioned in the first link, and signed up for a credit card. I built an excellent report and a score very near to perfect.
About 6 months ago I changed my main bank account. Let everyone who was collecting direct debits know the new bank details, and thought it be done.
However, my home broadband provide didn’t update their database properly and consequently failed to collect their direct debit. They immediately reported it to all three credit rating agencies, and my credit score nose-dived.
I got in touch with my broadband provider and after a lot of back and forth they finally relented and removed the mark from my report about 3 months later. My credit report was back in the very same state as before. Very shortly afterwards my situation changed very suddenly and very significantly, and I applied for a mortgage, and was accepted immediately.
So: (1) It’s important to know your credit report, so you know about potential problems when you still have time to do something about them. Fighting things can take months, building a good report/score can take years. (2) You can and should fight unfair marks on your credit report. (3) Fight this as soon as you can. You never know when you need a good credit report, and you have time to actually build up a score/report for when you need it.
Edit:
PS: I should mention that most banks will accept customers with low credit scores unless it’s really bad, but may not offer you an overdraft.
