I think like all things VE that bad news travels fast, so you'll get outraged people all over the place about the mess and petty crime that some members of some groups are responsible for, but hear very little about the ethnic origins of them when they raise £100,000 for charity. As a whole I really don't know, because as I said lots of things are exaggerated, lots of things aren't reported, none of us can possibly know the answer to your question.
To answer your other question, the families that winter with us and have done since before I was born are largely English Roma, with a couple of family members who have married out, and my partner (who has two degrees by the way and is the gentlest most law abiding person you could ever wish to meet) is Romanian Roma.
I have no issues with anyone decrying what an individual does, but massive racial generalisations are uncalled for and for most part I would offer inaccurate by and large.