What is some important social and historical context you need to know when studying Philip Larkin?

Philip Larkin was writing in a postwar England that had been heavily affected by the ravages of WWII, and his verse reflects the changing nature of British society at this time. On a personal level, Larkin was shy and suffered from depression; accordingly, many of his poems discuss feelings of hopelessness or lack of fulfilment, or of having failed to reach one's full potential. He was also based in Hull, a working-class town in the industrial north of England, and the people in his poems are usually hard-nosed, northern people from ordinary backgrounds. It was partly this preoccupation with the working classes that led Larkin to become massively popular among ordinary people, the sort of poet "even those who dislike poetry" liked. He was a popular choice for Poet Laureate, although in the event, this did not happen.
The post-war England of Larkin's poetic landscape was one where religion no longer provided the sustenance it once had, and many communities had been destroyed and reshaped by war. The new council estates were springing up in places where communities had suffered bombings, and young men back from the war struggled to adjust to civilian life. All of this informs the sense of desolation in much of Larkin's poetry, of a people who no longer understand who they are or what they should be doing with their lives.
https://www.poetryfoundation.org/poets/philip-larkin