Isn’t there a British company, Rolls Royce SNR, that is building small nuclear reactors?

They haven't actually built one yet. They have been selected as the preferred bidder here in the UK, but that's as far as it has got so far.

https://www.rolls-royce-smr.com/press/rolls-royce-smr-will-b...

https://www.gov.uk/government/news/rolls-royce-smr-selected-...