[1] Markham was the fourth son of Charles Markham,[1] Rector of Saxby All Saints (1866–1885),[2] and of Margaret née Barton, whose family owned nearby Saxby Hall and the lordship of the manor.
Algernon was born at his father's rectory,[1] and educated at Westminster School and Trinity College, Cambridge, where he was admitted a pensioner and matriculated at Michaelmas 1888, gained his Bachelor of Arts (BA) in 1891 and Cambridge Master of Arts (MA Cantab) in 1895.
[3] He married Winifred née Barne (a granddaughter of Francis Seymour, 5th Marquess of Hertford[4] and niece of Victor Seymour, sometime Vicar of St Stephen's, South Kensington)[5] and they had one son and four daughters.
From 1933, he was rector of St Andrew and St Mary's Church, Stoke Rochford (historically "North and South Stoke") with Easton, and he became, additionally, the incumbent (exceptionally called Dean) of Stamford at the end of 1936,[9] before his appointment to the episcopate.
[10] His appointment to become Bishop of Grantham was announced on 12 November 1937[11] — he succeeded Arthur Greaves, who was translated to the diocese's other suffragan see, Grimsby.