Last week I was wandering down towards Waterloo Place from Piccadilly and noticed that the area that once was St James's Market is surrounded by hoardings and in the process of being renovated.
So I looked up The Crowne Estate's site hoping to find that a street market might be included in the plans. Nope.
However, this pdf (from the Useful Docs section) includes some interesting information about the plans plus some history of the site.
For your delectation I am here including the lovely pics and historical info that can be found on page 7.