She might be thinking of air traffic controllers who, I believe, are not allowed to strike. Right now, I believe the police in the UK cannot strike, but the UKBA appears to fall under a more "civil servant" sort of umbrella.
I think it's important that people have the right to strike, and I think that the chaos and annoyance that it causes is exactly what the UKBA are going for.
The right to strike actually varies by state in the US (friends of mine in Florida could not, as public teachers, strike--I walked a few picket lines as a teacher in California), and there is a long history of labor activity/strike action in the US--just not recently. It gets tricky with "at will" employment laws and the like.