Was this a tribute to her by her lover, the 2nd Duke of Westminster? What better way to celebrate a romance, than by emblazoning it on the street-lighting?
In her brief biography on Wikipedia, he is said to have given her many extravagant gifts in the years of their affair, 1925-1930…
Sadly, the truth is more mundane, as is so often the case. The W and double C on the lampposts stand for Westminster City Council, who were responsible for the street lighting. It was designed for Parliament Square in 1951 – over 20 years after their affair – by the architect George Grey Wornum (source: WCC Street Furniture Manual, 1993).
Sorry, folks, it’s an urban myth!