No. You can give the CRA money, and they will take it, gladly, but this doesn't change the credit data they hold about you, which says (for example) that you skipped out on all the utility bills at a place you owned 18 months ago.
I've sat in on calls from consumers to a CRA when I worked there. The typical thrust of the call is that the caller believes they are a good person and so the records of them doing stuff creditors won't approve of should be purged, the CS agent explains that they can purge anything if the consumer sends them proof it is wrong, for example if the record says somebody went to County Court and secured a judgement against them for £800 then a letter from the court saying "Whoops, our bad, we wrote Michael Smith, 43 from Leicester in this judgement but we meant somebody else entirely" will get that erased from their record. But just calling and moaning about how you really wanted to buy a new car but your credit is bad doesn't change anything.
I didn't see any sign there was a way to short cut any of this by paying for credit reports. I guess if you don't remember all the times you didn't pay your bills then a web site that lists them is handy? But that seems like that's on you.
I actually had reports from all the big CRAs in my country, and the best ones (with the most comprehensive coverage, so, Experian, who also happened to be my employer at the time) basically just say this guy seems to pay for some basic utillities and he pays on time. And that's it. The worst ones are like "This guy exists, and we don't have good data so shrug".
The best way to begin "fixing" your credit? Which all of these companies will recommend, but it's no big secret at all? Register to vote.
Creditors prefer to lend to people who actually exist. Governments don't want people who don't exist voting. So register to vote and immediately confidence that you're actually a real person, with a postal address, shoots up.
The next step is easy for me but apparently lots of people find it almost impossible. Pay bills! Got a phone? Agree to pay the phone company to use the phone and then... actually pay them for it. Again, your credit worthiness shoots up because creditors want to get paid, and showing you have some idea how to actually do that part is a good sign.
Now, if you're trying to persuade somebody to lend you Ferrari 488 money on a Fiat Uno income, those two basic tips won't get you there. You're going to need to learn how to manage exactly the right levels of debt, what's recorded and what isn't, lots of tricks. But I assure you that you aren't going to learn that stuff by paying a CRA, because it's like learning how to clip out of bounds in a video game, the designers of the game don't even understand it well.