How drugged up is the City of London?

Not very, according to the latest Crime Survey for England And Wales. It appears the City is on a bit of a comedown.
Official statistics published today show just how far recorded drug offences have fallen in the City.
There were 440 recorded offences during 2013, down from over 1,000 in the 12 months to May 2006.
Drug offences in London generally continued to grow until the start of 2009, while use in the City had already stagnated, and use has dropped a lot further from pre-financial crisis levels.

The ONS offered no guidance as to whether the 2008 crash had caused the impact on the City’s drug dealers.
The City of London’s drop in drug offences is still impressive against a selection of other London boroughs, not quite as impressive as Lambeth, but moving in entirely the opposite direction to Richmond, where offences are still 50 per cent more common than they were in 2006-07.*

Drug use is falling across the country, but not quite as quickly as other crimes - there were 200,789 drug offences in England and Wales during 2013, a five per cent drop during the year, and down from a peak of 243,536 offences in 2008-09. In comparison, household theft dropped by 25 per cent in the year alone.
*For visual representation numbers included are all indexed to 100, but the total number of offences per borough varies a lot