Family missing in 1851/1861 UK censuses
I have an ancestral family who lived in England but doesn't appear in the 1851/1861 UK censuses. They do appear in the 1841 and 1871 censuses. This mystery has been unsolved for several decades.
John Williamson, a gardener in Cheltenham, married Ann Thomas in her hometown at Cradley, Herefordshire, on 17 Feb 1846. I have the civil marriage. They had two children in Cheltenham- Sarah in 1846 and Thomas in 1848. Their final child, Arthur, was born in 1852 in Leigh in the Malvern Hills. I have birth certificates for all of them, but no baptisms. In 1871 John Williamson died and this death was recorded, and later in the year the surviving members of the family appear in the census: https://familysearch.org/ark:/61903/1:1:VBJM-ZL1
Thank you in advance for any help