afaik the best approach seems to be to join a US-based company in the UK then ask them nicely to apply for a visa for you after a year. Then you're in the H1-B lottery.

AFAIK you need a visa first, most people I know that did this (myself included) first had a visa first: H1, L1, O1, etc. Then their employer sponsored a green card.

H1-B is the most common for tech workers, unfortunately due to quotas it can be pretty hard to get. Even if you get the job, your petition could be denied randomly because there were too many applications for the year.

I already have L1, but my employer won't sponsor green card. What are my options?

New employer using a different non-immigrant visa or EB-1.

IIRC L1 is not transferrable, so your best bet would be to try to snag an H1B at a different employer. It's much easier to do while in the US, so I'd ride out the L1 and apply for jobs between Nov and February to get in the H1B paperwork in for April 1st and hopefully get in the lottery. If it doesn't work on year, rinse and repeat. Depending on your occupation, O1 is a possibility, one of my friends switched jobs and went from L1 to O1.

The alternative if you're not married is to get your GC through your marriage if you have a US partner.

Yes, if you work on an H-1 your company can sponsor you for a GC. Many do.