I would use the term "classless" to describe our society, but make reference to John Majors speech and not the Marxist drivel.
Major was speaking not of class as the common man states but moreover class in relation to our meritocratic society.
Meritocracy as opposed to autocracy or nepotism is the key to our political and sociological interpretation of society.
Major did not state these did not exist, not denied their fundamental importance (re Durkheim, classic political sociologist) but he was talking about MERITOCRACY in relation to EQUALITY OF ACCESS to the institutional means to get on in life.
Yes if born an able-bodied, white male to wealthy parents your LIFE CHANCES are statistically much better, but Major was arguing that even a black, disabled women from an inner city had "access to opportunity"
Linked to the Tory idelogy of family values, hard work etc, I happen to agree whole-heartedly with Major on this one.
Life is what you make it, the opportunity is there and it is down to the INDIVIDUAL as oppose to SOCIETY to make these happen.
From political sociology this is the basis of INDIVIDUALISM (Tory) as oppose to COLLECTIVISM (Labour). Brting in terms like Thatchers NANNY STATE and you will be on to a winner as to what British society is really like.