It is clear from this play that class is a central theme that dominates the action and relationships between the characters. Note how Jimmy defiantly comes from the working class and how he hates the members of his family who are "pretty posh" just as much as he despises Alison's family. The class system in Britain, through the way that it clearly favours the upper classes at the expense of the lower classes, is clearly the reason why Jimmy is an angry young man. He feels so meaningless because of the way that his class background systematically renders him powerless and, he believes, insignificant. Even his attempts to do well in society seem doomed, as his degree is from the "wrong" university.
Note of course how Jimmy is compared to Nigel, who is clearly presented as being a stupid character, yet because he went to Sandhurst (the "right" place) has done well in life and is already a politician, tipped to "make it to the top." In particular note how Alison's mother is depicted as a character who is so consumed with class consciousness that she does everything she possibly can to stop Alison from marrying Jimmy. Thus class is shown to act as a barrier with nearly every relationship that Jimmy has in the play. The only person whom Jimmy is shown to be able to love without the stigma of class interfering is Hugh's salt-of-the-earth working class mother and Cliff. Jimmy likes Cliff because, as Cliff says, he is "common," pointing towards a similar class background.
Thus we can see that class is a dominating theme that prevents Jimmy from truly connectiong and loving a number of people in the play. It is a constant shadow that Jimmy takes around with him, preventing him from loving and from accepting the love that others have for him.
Osborne is one of the angry young men who criticized British society back then. As you have noticed, there is a class difference between the characters but all of them are grouped in one place in a Victorian building (stands for British legacy). They live together and their life is a bitter strife. Look at Jimmy and Alison, they love one another yet are unable to coexist. They stand in a way for a microcosme. They represent the British society of the time and highlight the failure of its post-war experience. That's why you must always have in mind that class discrepency.