I wouldn't think so Mungo. I think it was in last month's Sporting Rifle magazine that Peter Jackson of Jackson Rifles mentioned that you shouldn't use a centrefire moderator on a rimfire rifle because of the danger from accumulated unburnt powder suddenly igniting. In any case it is unlikely that a dealer will sell you a rimfire moderator instead of the centrefire moderator which you are authorised to acquire.
Well each to their own but Steve Kershaw specifically sells over barrel CF calibre moderators for HMR/WMR.
The extra volume of the chamber helps massively with the magnum rimfires.
I have used a PES T12 Scout on .22lr, .22WMR, .17M2 and .17HMR for over 5 years.
whilst the Lil'gun powder leaves ball residue everywhere I doubt this is "unburnt" as it is extremely fast burning by comparison to anything used in .2xx upward CF rounds.
Mine is strippable and there is more residue left from 10 rounds of 243 than a couple of boxes of .22 lr on night at the lamp
To the OP.
I had a "small bore" moderator on my FAC when I purchased the PES for my rimfire(s) (L&B)
when I measured the bore it was 6.5mm so I asked the police if I could use it on my 243 rather than purchase the "full bore" moderator I had a slot for. (why spend another £200 just for the hell of it!)
They said yes, technically I should have bought the PES under the "Full bore" slot despite its original purpose being rimfire, so they converted on the system. (FAC t be updated on renewal)
I now no longer own a "small bore" mod but use it on 5 calibres from .17-.243, i still have 2 slots for "full bore" moderators!
I dont doubt you could buy a similar mod to me and run it exclusively on your .22 (the police have no issue with multi calibre use that is why it is not a calibre specific listing on your FAC) but it will be heavier.
I use my PES on .22lr more than anything else and it is is very quiet, significantly more so that the SAK and PH I have tried.