As much as you have a point, I've been working in IT for years as well and I've only met one British worker in the US, and I think he's got at least a green card because he married an American girl. Just about everyone else I have ever seen working H1-B is Indian and boy do they fuck them over. As a white man who actually speaks a dialect of English that is considered civilized in the US, you are going to have a decent time of it. The only thing you need to worry about is idiots making too many Limey jokes and telling you that your spelling is funny.
The Indians generally have to worry about unscrupulous companies that bring them in, keep them in the dark and then make sure that they work under conditions that you could consider appalling. I can't tell you the number of H1-B colleagues that I know who have at one time or another had to worry about losing their job and then having to deal with being packed off back to India 5 days later because they are a guest worker.
The problem with H1-B is that it allows more bad than good. Clearly we want to have some guest workers like you over here to provide actual technical expertise, but most of these guest workers are doing jobs that Americans could definitely do and not even getting paid decently for it. That may be because we don't have enough IT people available to work over here, but I suspect that the supposed lack of IT workers is more of a situation where those said workers actually want to be paid US wages and treated like professionals.
Of course, the H1-B problem is one where many of us feel we are being unemployed in favor of cheap labor, but it doesn't change the fact that the program is allowing the guest workers to get screwed too, if they happen to be from somewhere sufficiently backward. That's just bad all around, and I see no reason that it should be allowed to continue as it has been.