I have been screwed over paying too much for my public transport a few times. The last 3 weeks they have auto topupped me with a disabled credit card, so now it evens out. I use a UK Blue Oyster Card and I'm thinking of buying a new one, in order not to have to pay the £60 of 3 weeks public transport. Would this possibly affect my credit score?
I have been screwed over paying too much for my public transport
How were you screwed ? Oyster has a daily limit, so you know how much you will be charged in a day. Not to be the morality police, but it seems you are more interested in not paying, rather than being overcharged.
Would this possibly affect my credit score?
Possibly yes. You would have provided your address while buying your Oyster card, so they have your details or else the credit card company might share your details. They might get a CCJ on you, if they decided to pursue, which you are liable to pay or else you will have it on your credit record. Or else you might face jail for not paying and a larger fine too.
Some links to change your mind. The first one is more relevant to your case.