Like many of his generation he enlisted during WWI, signing up on 24 August 1915 and served in France, firstly as a private soldier and then as a Lieutenant. After the Great War he did service in Ireland and then with the Indian Army in Iraq. I do not have a lot of detail and I may have got some of this wrong.
He saved money and when he had sufficient he enrolled at Wadham College Oxford in 1921 to pursue his ambition of obtaining a university degree. He managed to complete his studies in two years but since he was required to spend a minimum of three years there before the university would grant him a degree, he decided to take an M. Litt degree as well. Thus equipped he found a job with the Dictionary of National Biography at £250 a year - quite a good income.
A career in politics seemed to beckon. He contested a seat in 1924 for the Labour party and in 1928 he was selected as the Labour candidate for Rochester, where he won election in 1929. Markham was a supporter of Ramsay McDonald, who was regarded as betraying Labour by entering into a coalition with the conservatives. Markham therefore became member of the National Labour Organisation and served as MP for South Nottinghamshire from 1935-45.
During WWII he served as a captain and retired in 1945 with the rank of major.
In 1950 he contested the Buckingham seat for the Conservatives against Aidan Crawley the Labour MP. He lost that election by won in 1951 by a narrow margin of 54 votes. It is curious that the Labour party at this election was represented by the patrician Crawley, while Markham, from a much humbler background represented the Conservative party. He held the seat until his retirement in 1964.
His interest in history ran deep and after WWII he began to write his books. A History of Stony Stratford was first published in 1948 in collaboration with Francis Hyde, then a young Professor of History at the University of Liverpool. Hyde wrote the first half of the book up to the end of the Tudor period and Markham brought the history to the present day. He followed this with the Nineteen Hundreds in 1951, about the first decade of the new century in Sony Stratford.
Before the war he had compiled reports on ar galleries and museums in the British Isle, then Australia and the South Africa. His British Isles report was updated and published as a book in 1948 - Directory of Museums and Art Galleries in the British Isles.
In 1930 he wrote a book called The History of Socialism. It was published in 1930.
On his retirement from the House of Commons he started to pull his collected materials together to form his magnum opus History of Milton Keynes and District, published in two volumes in 1973 and 1975. At the time of writing Milton Keynes, the new town, was on the verge of coming into being and he thought this would be an appropriate title.
In addition to his books he published many articles and valuably transcribed and translated the Wolverton Manorial Documents held in the Boolean Library. This is on typed sheets of paper bound in a single volume held at the County Archives in Buckingham. He was also a founding member of the Wolverton and District Archaeological Association.
He died on 13 October 1975.