Betjeman's reputation suffered, at least in Britain, because he was popular and in Britain poets can't be both popular and good. It's a pity because there are probably people who would read him with pleasure who don't give themselves the chance. Was he in the Auden/Eliot class? No, not quite--but he was very good. He appeared to write ordinary poems for ordinary people--but, in fact, there was nothing ordinary about them at all.
Betjeman is my favourite poet. He dared to be funny and suffered critically because of it. You never have to search through the pretentious bollocks to discover the meaning - it's there on the page, for everyone to see.
The title is a tip off. Trite, though it is, and it is, A NIP IN THE AIR is a common phrase describing a common experience in a slightly poetic way. What is a nip, after all, but a bite? Air has no teeth to nip you, and so, a metaphor.
It is easy to understand why Sir John was beloved in his time, for in this collection he writes about those trite and familiar British institutions, such as rail journeys, the church, attending funerals, the work place, and the countryside. Trite subjects written of in unchallenging verse. It is all very pleasant, how could be be otherwise, but there is little in this collection that takes readers to a deeper level of meaning or insight. The institutions are not challenged or questioned, merely remembered, and pleasantly.
That is true for the vast majority of the poems in this collection, which include some celebratory poems written after Sir John became poet laureate. If the other poems dance on the cliff of trite, these latter poems fall over the edge. They are truly terrible.