the H1 does not automatically allow one to stay permanently. H1 is a permit an American company can obtain for someone they want to hire. In other words, you could not get one for yourself and then get there and go look for a job - you need to have an employer first, and they apply for the visa for you. Once you get there, if you are employed for a period of time (not sure how long - a few years) and you want to change juobs you can apply for permanent resident status, but there's no guarantee you will get it granted.
Before moving to the UK I had occasion to entertain the possibility of hiring a UK citizen to work for my company. As it turned out we decided not to but I did do the research.
Plus, when my husband was transferred here (London) we had to do a little more research on ther rules regarding work permits in the US and UK as well.
This is how I know.
ps most of my uk buddies have been made redundant in the past year. My american friends are all working. who's got an employment problem...?