In the 1950s in England, life had settled down from the trauma of WWII and had returned to the "status quo". The class structure that had dominated the country since the 16th century and the Victorian social standards that had - but had not - been abandoned, were firmly entrenched. A conflict existed between the "appearance" meant for society and the true nature of a person's feelings - do those feelings really exist if the person is too formal to express them?
Jimmy expresses himself a bit too freely, but as the protagonist, he is used to show the audience the need to let go of apathy and reserve and to "feel". Osborne wanted to demonstrate the need to reject the old "stiff upper lip" English stereotype in favor of a more fluid and interactive expression of anger, fear, love, etc..