I assume you aim to get a US job via H1B visa, then become Permanent Resident (AKA Green Card). Did you read up about it? This is long and complicated process (Green card can take few years, unless you marry US citizen :-) ), but can be done (I did). It will not be easy to "undercut yourself" paywise because employer applying for your Green Card is expected to advertise your position AND to pay prevailing wage.
Good start is to be either hired by UK subsidiary and get transfer, or getting real important skills in something. Good option to showcase your skills is any relevant open-source project, because it is open way to show your skills and get peer-evaluated.
You cannot pay your employer to apply for Green card (would be not only expensive but also illegal). There are other investor type visas you may consider (if you can afford it).
Another option (no personal experience) would be to immigrate to Canada, which has saner and more predictable immigration process: you get points for skills, age, language, relatives in Canada etc, pay the fee. Points are known, you can count your chance yourself. As Canadian citizen, you can get TN visa to work in USA. Or travel world, with cheaper health insurance than in USA. :-) Also, IIUC you don't need a sponsor to immigrate to Canada: if you have enough points and your application is approved, you travel in and start looking for a job.