Is the Coalition Government actually quite left wing?

There's long been a problem with definitions of left and right wing.  Hitler called himself a National Socialist, the BNP says it would like more public ownership too.  Where did the phrase 'British jobs for British workers' come from?

The outgoing Labour Government made a case that all should benefit from a welfare state.  Thus Child Benefit payments ended up in the hands of many middle class households.  University education, which overwhelmingly favors middle class kids, has been subsidized over its true costs for some time. Cuts in these areas are much more likely to affect wealthier families.  Could this be deemed to be 'progressive' then?