I have upgraded my wall warts, mostly for fear of noise, but having taken apart some Rega mini accessories I have to agree, that needs to be replaced. For the same reasons, I recommend Pro-Ject electronics over anything made by Rega. Better value and better attention to power supply noise abatement:
Still what most would call "entry-level" though, if you are serious about vinyl you'll probably want something even better.
If you do have other devices worth an upgrade, I recommend the iFi wall wart replacements:
I use them mostly because I feel they prevent more noise from getting back-fed through the AC supply to other equipment. I use them on my streamer, DAC and Ethernet swtch.
Seriously though, if you are investing right now, a new phono stage is probably your better way to go.