In the US, generally, the company applies for your visa. So you need to get a job offer first from a company that loves you so much that they'll apply for a visa for you, and wait the typical 6 months it takes for the visa to get processed.
The best US work visa right now is the H1B. It lets you change jobs to any company (in your field), provided that company is willing to do a small amount of work to "transfer" the H1B visa.
There's another visa called the L1 visa for intra-company trasnfer, but it sucks. It locks you down to the company. You can't change jobs, and you get kicked out if you ever get let go from that company.
You've asked your question at a good time. Every year, companies apply for the H1B visa on April 1. There is a limit of 85,000 visas per year, and if the gov receives more than 85,000 H1B applications on April 1, they perform a computer randomized lottery and randomly select 85,000.
If you want to move to the US, this is the time. As a UK citizen, you can visit the US without a visa, and stay for up to 3 months. Ideally, fly in on Jan 1, and stay for the full 3 months. You could sublet an apartment for 3 months on craigslist. Then apply, apply, apply. While traveling on ESTA, do not say you're going to apply for jobs. It is a legal grey area, and the interpretation of the law varies on whether looking for H1B employment is considered "immigrant intent" (as the H1B is a temporary 6-year non-immigrant visa). What this means is that there is the possibility that you could get denied entry at the U.S. airport you arrived in under Immigration and Nationality Act Section 214(b) for having "immigrant intent", get sent back, and receive a 5-year ban.
If you are a good software developer, you should have no problem finding a company willing to apply for you. Once a company says they'll apply for you, you just need to go back to the UK and wait for the results of the lottery.
You'll know if you won the lottery by June/July. Last year, they got 233,000 application, and they chose 85,000 out of that randomly. You could say your odds of winning are 1 in 3. There might be even more applications this year.
If you don't win the lottery, there's two options:
1) Re-attempt this whole process, and try the lottery every year. You'd have to move to the US for at least a month or two, ideally in January, February or March.
2) You could get a job at a US company in the UK, and ask for a transfer to the US. If it works out, you'll be in the US on a L-1 visa. This visa doesn't allow you to change jobs, and requires you to leave the country if you ever leave the company. But if your job is with a large stable company, that shouldn't be too much to worry about. Now there's two routes you can go down from here:
2a) Ask your company (i.e. the sponsor of your L-1 transfer visa) to apply for an employment-based green card. The green card process can last anywhere from 1 year to 6 or 7 years (or more), depending on what category you were put in, and what country you were born in. You are, again, locked to your company during this period.
2b) You can looks for jobs in January-February-March period while you're in the US on the L-1 visa. The company will have to apply for an H1B visa for you. If you win the lottery, they switch you over from your old L1 to your new H1B. Once you're approved for the H1B, you can switch to other jobs fairly freely. (There's still paperwork to change jobs on the H1B, but 70% of tech companies in the US are willing to do it.)