Chav may have become synonymous with socio-economic status, but it has far more to do with how you conduct yourself and the way that you treat those around you.
There are loads of monied sorts around my way who could be said to exhibit the traits that we associate with chavs. Brash, rude, no respect for others, resorting to entirely unjustified levels of violence and aggression over the pettiest of incidents.
It is not some kind of catch-all term for the working classes (how would you define who they are in 2012 anyway?) and it isn’t restricted to white people either. Personally, I think it’s somewhat insulting when middle class liberals take third party offence on behalf of whoever they imagine the working class to be. The chav culture (and I use the term loosely) is anathema to traditional values of self-reliance and hard work (not that these were exclusive to the working classes).
The people I know who use the term most frequently (and with the most venom) aren’t particularly wealthy, often living on or significantly under the average wage, but who wouldn’t dream of giving up on life and/or outsourcing responsibility for every facet of their existence to organs of the state.