Job question for UK folks

In the UK, when you provide references for a new job, is it typical that you need to give your current employer as a reference? I'm applying for a job for a company based in the UK but they are opening a new US branch, they are requesting references but no offer yet. I've heard in the UK they expect to speak to you current employer, but in the US thats pretty much unheard of except maybe on rare occasions upon reaching a formal job acceptance as a contingency. Maybe because we have pretty much zero job protection in the US so it's risky for them to know youre looking elsewhere in case the new offer falls through.