History
It was originally founded in 1864 as University College Mathematical Society, one of UCL’s student societies, for the pursuit of mathematical knowledge (H. Hale Bellot, University College London, 1826–1926, 1929)
Soon afterwards it became known as the London Mathematical Society
Augustus De Morgan’s son George was one of the student founders, and he himself, unsurprisingly, was its first President (H. Hale Bellot, University College London, 1826–1926, 1929)
The cofounder was Arthur Cowper Ranyard, pioneer astronomer and son of Ellen Ranyard, who founded the Biblewoman movement (Oxford Dictionary of National Biography)
In 1877, according to The Times, the Hon. Secretary was Robert Tucker (1832–1905), then of University College School (The Times, 11 December 1877)
It was granted a royal charter in 1965
In 2009 it rejected a plan for the creation of a new unified mathematical society with the Institute of Mathematics, www.newmathsoc.org.uk (opens in new window); the Institute members had voted overwhelmingly in favour but the LMS voted narrowly against

What was reforming about it?
It was an avowedly nonhierarchical, nonbureaucratic society devoted to the scholarly promotion and prizefunding of mathematics, which it remains
Where in Bloomsbury
The earliest meetings of the Society were held in UCL, but it soon moved out of Bloomsbury to Burlington House, Piccadilly
However, in 1998 the Society returned to premises in Bloomsbury, when it moved to De Morgan House, Russell Square
Website of current institution

Books about it
None found
Archives
Records of the Society have been deposited in University College London Special Collections (ref. LMS), and include correspondence of the Society’s officers as well as mathematical papers; more details are available online via UCL Special Collections (opens in new window)
