I think that isn't Markham but Henry Markheim. His overseas birth registration at at Smyrna . https://www.ancestry.co.uk/sharing/19400417?h=6a485c&utm_campaign=bandido-webparts&utm_source=post-share-modal&utm_medium=copy-url
His father, Harrison Markheim was a missionary there.( Henry Foster, Oxford Men and their Colleges 1880-92)
The 1901 census (more clearly written than the 1871 but is also misindexed as Markham) has mother Eliza born Somerset.