Yes, it is. There's a fairly big "JDM" (Japanese Domestic Market) car interest in the US, and I've seen plenty of them registered, insured and driving here. I think getting them emissions certified since the standards are all different is a bigger hurdle when importing than anything else, and that wouldn't apply here.
Edit: Also, the other direction, you'll see a lot of LHD cars in the UK where American troops are deployed. That's a pretty specific loophole, but I remember getting a lot of confused looks driving around.
It's not really a loophole is it? European drivers are welcome to drive LHD cars into UK via boats/channel tunnel just as we can take British cars to the rest of Europe, American troops just happen to be a significant group who take advantage of it being completely legal.
As to the confused looks, I would hazard a guess (having lived near a US base in the past, now not but still see EU cars every day) that they were over your choice of make/model (e.g. a Chevy of a type that no Brits buy), rather than driver side. Maybe I'm wrong and lots of people give weird looks because of the driver side, but personally I've definitely stood staring at cars that looked weird to me and were clearly US imports, but if I see a car that's common in the UK it's not that interesting noticing when there's a foreign version on the road here.
edit: oh and number plates too. American style is obviously much less common than even most old European country styles, yet alone the more standardised versions of the past couple of decades. So even if the model of car is the same, seeing an EU plate you think "they probably drove it from mainland Europe" which is pretty common for holidays, work, or just people relocating and keeping their car, whereas seeing a US plate makes you wonder who cared enough to ship it all the way here.
I guess I used "loophole" because the whole program is a loophole. Typically exempts you from inspections, no international drivers license needed, you buy coupons that relieve the fuel tax, we use weird number plates as you mention (not the ones from home, but military off-duty plates). I had an old LHD Opel Rekord from Germany when I was in the UK, like this one: https://en.wikipedia.org/wiki/Opel_Rekord#/media/File:Opel_R...
Edit: Also, the other direction, you'll see a lot of LHD cars in the UK where American troops are deployed. That's a pretty specific loophole, but I remember getting a lot of confused looks driving around.