The obvious first question is "have you published". That's not enough as I well know from personal experience, but it is almost essential for validating your degree. These days, in the UK, if one's degree is not from Oxford or Cambridge or a handful of other universities depending on field, or Edinburgh (Scotland) or Queens (N.I.) things are tough. Not every minor or state university in America is recognised as equal, in part because of the disaster that making "universities" out of all the polytechnics, some of which rate rather badly in the way of community (ex-junior) colleges in the USA.Let me second Joppa's suggestion about getting some work experience in the US before trying to relocate overseas. It was a few years back that I made my move, but having some US experience can really make you more employable as a foreigner.
Just about all European countries these days have their highest unemployment among young people and those looking for entry-level positions with brand new qualifications. It can also help to have some form of experience on the job that is "unique" to the US job market - or in short supply in the market in which you are looking.
Fortunately science speaks for itself. But even so: my daughter, with a First from Cambridge in medicine, scarcely needed an interview to get her first quasi-research junior house doctor positions. Whereas others had to go abroad.
Read up as much as you can about the academic environment here. And be aware that scientists are leaving here for more money in the USA. Even Paul Dirac left - and he was Lucasian Professor. OK, I admit it: it was to rejoin his elder daughter Mary in Florida...
But maybe you're not scientists?