Their very conservatism is secondhand, and they don't know what they are conserving.

Davies is criticizing a kind of unreflective traditionalism: people who call themselves “conservative” not because they have examined inherited institutions and chosen to preserve particular goods, but because they have absorbed attitudes and slogans from their milieu. “Secondhand” suggests borrowed convictions—opinions worn like hand-me-down clothes—while the closing clause (“they don't know what they are conserving”) implies ignorance of history, principles, and the actual content of the traditions invoked. The remark also hints at Davies’s broader satirical interest in cultural pretension: the pose of seriousness or fidelity to the past can mask intellectual laziness, and the rhetoric of preservation can become empty when detached from understanding.