I can understand why you'd think that if "gypsy" means to you what you described, but I think what people usually mean when they say that is that the Jews tend to get all the attention and sympathy whenever the holocaust is mentioned, and that we shouldn't forget the other persecuted groups. I'm sure I remember a news story from a few years ago where a representative of the gay community wanted to be involved in a holocaust memorial ceremony and the Jewish leader kicked up a fuss, or something like that.

I've never had any contact with gypsies myself, but as far as I'm aware the main problem is that they show up in large numbers to park their caravans in the field next to you, possibly make noise late at night, and after a while go away again leaving behind a great big mess for the locals to clear up.

I don't know if they "live off the state", but I believe that's the perception. Bear in mind, though, that many people in Britain seem to think all minority groups live off the state, including the same economic migrants who are "taking our jobs" (even though the two are mutually exclusive), and the asylum seekers who are forced by the system to live off the state precisely because people don't want them to "take our jobs". These people are also unable to distinguish between the concept of "asylum seeker" (people who have fled persecution in fear of their lives) and "economic migrant" (people who have come here to earn higher wages than they can get at home), probably due to a one-time trend in the papers to write about instances of the latter pretending to be the former. So the fact that it's the perception doesn't necessarily mean a lot. As Paul said, it's likely that gypsies aren't sufficiently integrated to know how to apply for benefits. A lack of a permanent address also makes extremely difficult to claim them.