Ironically, other countries (former British colonies) have more access to US "specialty occupation" working visas than the UK does -- none of these are H1-B.
Canadians and Mexicans have TN, Australians have E3, Singapore and Chile have H-1B1 (a subcategory of H1-B but with its own quotas).
I have to correct myself slightly -- the Brit engineers I do meet in the US often come here on an L1A/L1B intra-company transfer from a British subsidiary. So that's one path.
But yes, the visa path for UK citizen to accept a direct job offer is much more limited.
Canadians and Mexicans have TN, Australians have E3, Singapore and Chile have H-1B1 (a subcategory of H1-B but with its own quotas).
https://www.uscis.gov/working-in-the-united-states/temporary...
Most foreign engineers in the US (outside of H-1Bs) are actually Canadians.
But there are no easy visas for the UK.