The Royal Society was founded in 1660. (TV: The Happiness Patrol) The Seventh Doctor had a membership (PROSE: The Room With No Doors) and River Song was an honorary member. (AUDIO: The Sonomancer)
Madame Vastra and Jenny Flint went to a lecture by Fabian Solak at the Society in the 1890s. (AUDIO: The Cars That Ate London!)