No, there’s no quick fix, but it’s not that important. You’ve been able to use purchase finance, obtain overdrafts and a credit card, there’s no reason to be concerned about your credit worthiness. An account rejection at your age is unimportant, it’s inconsequential and not worth worrying about.
The time when good credit starts to matter in a serious way is when it comes to mortgages, but even then there’s nothing you can (or should do) beyond use the credit you have available to you responsibly. Avoiding negatives (missed payments, payday loans, CCJs) is most important when it comes to mortgages, having an extra paid off finance account is not going to be the difference between a mortgage or not.
Personally, I would consider the risks associated with financing a bunch of things in aide of “building credit” to be higher than the benefits of “better credit”. Credit has more than just financial costs, it’s mentally taxing and limits your flexibility in life. Credit should be used as a tool to achieve meaningful things, it shouldn’t be used to improve a meaningless score.
Editing to add: put simply, 5 years of one credit account repaid in full every month is better than 1 year of 5 credit accounts repaid on time.