Hi Liav,
I've owned the 22's for the last four months but recently upgraded to the fact 8's. The 22 is a great speaker but to get the best out of them they do excel when driven by more powerful amps.
The first time I heard the 22's was alongside the Kef LS50's. they were both being driven by Musical Fidelity M1 HPAP pre and the M1 PWR power amp which puts out 60 watts per channel, so quite close to what your Rega Brio R puts out. The Kefs sounded great but a little too boomy for my liking (incidentally, I only use my sub at home when watching films and not for listening to music). The 22's sounded good too but with this set up they didn't sound like they were more than twice the price of the Kefs. Now taking in the big price difference between these speakers I knew something wasn't quite right so I asked the dealer to connect up their best integrated amp which turned out to be a Leema Acoustics Tucana 2. Wow, the difference between the Kefs and the 22's was like night and day using the Tucana which puts out 148 watts per channel. The 22's were so detailed and sounded incredible with a nice tight bass. The soundstage they created for their size was I thought, quite amazing. Now I could hear why the 22's were more than twice the price of the Kefs. Incidentally, I was using my own MacBook Pro as the source playing Wav files.
After listening to the Kefs and 22's I asked the dealer to swap the Tucana 2 over and to connect up a Roksan Caspian M2 integrated amp which puts out 85 watts into 8 ohms. The difference in sound quality compared to the Tucana 2 was very noticeable and had nowhere near the refined sound that the Tucana 2 produced. The sound with the Roksan just didn't have the same clarity and detail as the Tucana. But again, the Tucana 2 is more than twice the price of the Roksan so you'd expect the difference to be clearly audible, which in my case it was. It was interesting to listen to the Kefs and the 22's with three very different amps that went up the scale in power and price. I read quite a few posts from people who say that amps don't make much difference to the sound quality but personally I disagree with that.
My advice would be to take your Rega amp with you to audition the 22's to really see how they sound using your kit. And if you decide to do what I did by listening to more expensive and powerful amps with the 22's then do so at your peril, as when I did, there was no turning back and it caused a bigger dent in my wallet than I had initially anticipated. But the end result for me was worth it. Unfortunately for me, four months into owning the 22's, I ended up auditioning the fact 8's and the impression that they made was too much to resist.
So yes, going back to your original question, your Rega Brio R will drive the 22's but I don't really feel that you will be getting anywhere near what the 22's are capable of sounding like. I'm not familiar with your amp, I know, so I may be wrong, but based on my auditioning experience I'd suspect that if you improved your amplification then you'd get a lot more out of the 22's. This is of course, my opinion only and what counts more is what you hear and feel.
The 22's really are a great speaker and produce incredible detail and amazing sound, but the better your amplification, the more you will get out of them. As with all things, it comes down to your own personal view and what you like and how much you want to spend.
Good luck and I hope you enjoy hearing the 22's as much as I did when I first heard them.