The problem is that I don't think there is a visa you can get that will allow you to do what you want to do.
- A business visitor visa would be the first thought as it's temporary, valid for up to 6 months, but it does not allow you to perform any actual work except for doing things like attending a conference or meeting, performing as a musician, taking part in a sporting event, doing academic research etc. You can't work full-time for a UK company on this visa.
- So I think an actual Tier 2 work visa would be the only option, but that would require that the UK company becomes a Tier 2 visa sponsor (and it can take several months for them to register as a sponsor and will likely cost over £1,000, if it's a decent size company)
AND then to hire you, they have to prove that either:
1) the job you will be doing is listed on the Tier 2 Skills Shortage List and pays a certain salary (
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/423800/shortage_occupation_list_april_2015.pdf)
OR
2) the UK company has advertised the job across the entire UK and all other EU countries for a certain number of weeks and they have not found a single suitable candidate for the position (out of 27 countries and 500 million people)... so they have no choice but to hire you from the US instead of a UK/EU citizen.
They directed him to have me contact a) the international help desk or b) the British embassy to see whether they can help. I haven't done this yet as I'm not quite sure what I should say that would help.
Honestly, I wouldn't bother contacting either - the immigration help desk is notorious for not knowing what they are talking about and therefore give bad or incorrect advice, and I don't know if you can even contact the British Embassy - they would probably just direct you to the helpline.
All the official information about the visas and how to qualify for them is on the UKVI website:
Visitor visas:
https://www.gov.uk/standard-visitor-visa/overviewTier 2 work visas:
https://www.gov.uk/tier-2-general/overview