All the info is contained in AIC (Mauve 134) 91/2004 which is available on the ais website.
Three restricted areas are being established around Hyde Park, City of London and the Isle of Dogs the upper limit of which is 1400 ft AMSL. These areas do not affect helicopter traffic on route H4.
The conditions applicable to flight within the Restricted Areas are contained in AIC (Yellow 148) 87/2004, again available on the ais website.
Hope this helps.