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Westminster Bridge was opened in 1750; Blackfriars Bridge in 1769 and this meant this area of fields was ripe for development. Part of Robert Mylne's work was the construction of St George's Circus and Blackfriars Road to connect his Circus to his new bridge. This was the first circus in London, following their introduction to the UK architectural landscape in Bath, where the (King's) Circus had been, at least partly, inspired by nearby Stonehenge. 

Mylne also designed the obelisk, proudly specifying how close this site is to significant London locations - important if the area was to become popular and make money for the developers: location, location, location.

A number of websites (possibly all originating from Wikipedia) give different dates for the following events but we have taken the Listing text as the most likely to be correct. In about 1897 the obelisk was removed to make way for a clock tower celebrating Queen Victoria's Diamond Jubilee. Getty have a photo of the tower from the 1930's showing the surrounding buildings which they suggest were largely destroyed in the WW2 Blitz.

The tower was itself demolished in the late 1930s to free up traffic movements. Meanwhile the obelisk, listed in 1950, had been biding its time in nearby Geraldine Mary Harmsworth Park and in 1998 it took up residence again at St George's Circus. Sadly we cannot find a picture of the obelisk during its sojourn in the Park.

In 1899 the crypt of nearby St George the Martyr (at Borough tube station) was cleared and almost 1,500 coffins were moved from there to Brookwood Cemetery (as were graves from a number of other overcrowded London churches). A copy of this obelisk was used to mark the location of the St George re-burials. Wikipedia has a photo of what's left if it.

Diamond Geezer is essential reading for those who wish to know more about this area.