In the UK, “Asian” (in common vernacular) usually refers to descendants of India/Pakistan/Bangladesh/Nepal/etc.
In the US, “Asian” usually refers to descendants of Chinese/Japanese/Korean/Vietnamese/Thai/Filipino/etc.
What pops into my mind is that the US is closer to what you would call east Asia than it is to India, and, of course, Britain has particularly strong historical ties to India/Pakistan etc. So that might also be a factor.
Still, there must be many reasons why asylum seekers in Calais are trying to get to the UK, when they passed through a number of EU countries first.
In 80s and early 90s Punjabi movies and songs "Inglaand" may have been popular, but since the 2000s "Kaneda" has the goto choice.
Most South Asians you tend to see now are there for educational tourism and will eventually move to Canada or back to India, or are from business/political backgrounds looking for a backup passport should they be prosecuted for crimes (eg. Nirav Modi, Lalit Modi, Vasundhara Raje Scindia, Vijay Mallya), though even the US ranks higher for them but they wouldn't be allowed in the US due to background checks or past criminal records (eg. Lalit Modi's attempted stint as a coke dealer at Duke). That said, they definetly send their families to the States. For example, Amit Shah's sisters live in Schaumburg IL and Imran Khan's sis is in the Tri-Valley.
The fact remains UK has one of the best university systems and best opportunities for skilled work outside of the US. Yeah the Tory gov is trying their best to destroy the country but this kind of institutional bias is hard to wreck. It's very similar to the US - which has an amazing university system that continues to prop up the economy over the long term, despite how destructive/insane the government policies are.
I'd also argue that for lots of immigrants, things like the NHS and general safety net make the UK far more appealing than the US. Also if you're from a former British colony, it feels a lot more familiar - so you see large numbers of east asian nationals who prefer to immigrate to the UK over the US.
On top of all that, it can also be significantly harder to get a visa to live in the US.
1: https://commonslibrary.parliament.uk/research-briefings/sn06...