Publisher and philanthropist, Measom was born in Blackheath, Kent, on 3 December 1818, and baptized in St Alfege, Greenwich, on 12 July 1819, perhaps the eldest of the five children of Daniel Measom (b. c.1790), carver and gilder, and his wife, Mary Ann, née Coventry. He was educated at a preparatory school in Blackheath, but the early stages of his career are obscure. On 27 January 1842, when he married Sarah (1820–1865), daughter of John Hillman, fishmonger, Measom described himself as a tailor. Later in that decade he advertised his services as an engraver, an art in which he evidently had some skill. In 1849 he published a pictorial work of his own devising, The Bible: its Elevating Influence on Man, in an album of six wood engravings depicting a drunkard rescued from his addiction by exhortation.
About 1850 Measom acquired a new interest as a railway topographer which absorbed much of his energy over the next twenty years. It was furthered by his artistic skill and his sense of the power of advertising, both of which appeared again in The Crystal Palace Alphabet: a Guide for Good Children (1855), and Light from the East: Tales Moral and Instructive of Oriental Origin and Character (1856). By then Measom was describing himself as the author of the Official Railway Guides, the first of which had appeared in 1852 as The Illustrated Guide to the Great Western Railway. From the first Measom's guides were addressed to the traveller, and insisted on the practicalities of travel by rail. Passengers were advised to inquire about the services available, to consider their best route, to note where they had to change trains if the service was not direct, and to prepare themselves for their journey by equipping themselves with necessities. It evidently occurred to Measom that the standing of the guide could be improved by invoking the authority of the railway company. The guide to the Great Western was followed in 1853 by The Official Illustrated Guide to the South-Eastern Railway and all its Branches, and every succeeding volume was distinguished as ‘official’, with the company's arms on the cover and a list of the directors and officers as well as a description of its principal undertakings. By 1867, when official illustrated guides to the Irish Midland, Great Western, and Dublin and Drogheda railways appeared, the whole network was covered. Journeys to Paris and the Île de France by the Northern Railway of France were described in a supplement to the guide to the South-Eastern Railway in 1859. The guide to the Great Eastern in 1865 included a map showing connections to Naples, Vienna, and Danzig, and accounts of Antwerp and the principal towns of the Netherlands.
The sightseeing excursions proposed for a stay of six days in Paris imply a more self-assured and enterprising readership than the earlier advice on finding the railway station and buying a ticket, but the guides themselves, always sustained by their practical nature, changed as their reputation grew. From the beginning the traveller could be expected to look out of the train windows and draw some pleasure from the passing spectacle. The guides therefore described places of interest on the route, as well as at the final destination. Antiquities were well documented, and in an age before photographs could be simply reproduced Measom's skill as an engraver stood him in good stead. Commercial information was another matter. Local directories had to be collected and were not of an assured quality. There were few provincial libraries, and chambers of commerce were still inchoate. Measom, who was a fellow of the Royal Geographical Society, spoke of having travelled over the entire system, and he evidently made useful contacts wherever he went—with manufacturers of soap, chemicals, and carriages, and in Birmingham over the whole range of the city's products, including pen-nibs. In other places he singled out correspondents whose own interests were served by stocking and selling the guides, and who could inform him about the local market. The finished product attests only baldly to an endless series of inquiries, visits, and negotiations.
The guides came to an end with the 1880s, though they were revised and reissued. Measom continued to publish engravings in his later years, but having achieved a comfortable ease and competence he devoted himself to philanthropic works. He became chairman and for some time treasurer of the Royal Society for the Prevention of Cruelty to Animals, and was a promoter of the charity later known as the Battersea Dogs' Home. He was also active in supporting the hospital, later the Royal Marsden, and argued strongly for the use of the title Cancer Hospital at a time, long enduring, when such bluntness was superstitiously shunned. Following the death of his first wife, in 1867 he married Charlotte (d. 1911), daughter of George Simpson. There were no children of either marriage. He was knighted for his public services in 1891 and became a justice of the peace for Middlesex. He continued to be active to the end of his life, and under recreations in Who's Who remarked simply and convincingly ‘Never had time’. In many respects he was a perfect model of his time. He died at his home, St Margaret's Lodge, Isleworth, Middlesex, on 1 March 1901.