Here's the stats on UK aliyah to Israel. You'll see that it's more than doubled since 2002, although still under 1000 a year. And that doesn't count people to move on an extended basis to Israel but don't formally make Aliyah.
I can only speak anecdotally about the U.S. But I do live in NY. And there are more Brits around today then there were 5 years ago.
Also keep in mind there are about 280,000 Jews in the U.K., or about 1/20 the number there are in the U.S. But aliyah from the U.K. is only about 4 times smaller. So, in percentage terms, British Jews are about 5 times more likely than American Jews to make aliyah (although still much smaller than 1% a year). That might have to do with higher levels of religiousity and/or Zionism. But hostility to Jews could certainly be a factor as well.