Did the Blitz really unify Britain?

From the BBC

"The defiance of Britain as it endured eight months of German bombing 70 years ago is etched on the collective memory and immortalised in the phrase "Blitz spirit". But does this image of national unity tell the whole story?

Even for those lucky enough not to have been there, the sound of the sirens is enough to evoke those nights of 1940 when British cities were under constant attack."