I see two major hurdles which you'd need to overcome.
Firstly, you would need to convince the company that the not-insignificant expense in both their time and money would be outweighed by having you working on-site in their office in the USA instead of remotely from London.
Secondly, the company would have to convince the US Dept of Labor that there are no suitably qualified American citizens (or legal residents) who are willing and able to take up this on-site job.
I think the DoL is likely to wonder what's changing in the job description which now requires an on-site presence. You've presumably been performing your duties remotely perfectly well up until now, and with the current state of affairs, many companies are changing their business models to locate more of their workers remotely instead of on-site wherever practical.
With that in mind - even if they can make a case that they need someone in this role to be located in the US, how would they believably take the position that there's no-one suitable anywhere in the US, or even in their state?
IMO, this unfortunately would probably be a waste of time to pursue, although there's probably no harm in asking.
I moved to the US with an H1B a little over 8 years ago (and now have a 'green card'), but I'm almost certain that if I were trying this today I'd fail due to the fact that most of the work I was doing then really could have been done remotely (since that's what I was already doing). My current role requires me to live near to one of the company office locations and be available to work on-site for up to 50% of the time though, so in this position I think my chances would be much higher.