There was a time when ‘dropped kerb’ meant exactly that, in other words the pavement was on the level except for a narrow strip at the kerb-edge where it dropped. What we have these days could better be described as ‘dropped pavements’. Why does it matter? It matters because with the old design pedestrians, and buggy/wheelchair users had a level surface for the majority if not all of the width of the pavement; with the modern design much of the pavement is on a slope with frequent abrupt changes in level for pedestrians. Here are some examples, firstly showing traditional dropped kerbs:
A traditional dropped kerb beside a vege – totally flat pavement
A traditional dropped kerb without a verge – 80% of the width is flat
Compare that with a modern ‘dropped pavements’, where the entire width of the pavement is on the wonk with steep entrance and exit ramps for pedestrians across much of its width. Here are a few examples:
A dropped pavement (err… plus modern wheelie-bin) – much tougher for many pedestrians
In this example 1/3rd of the ‘pavement’ is underwater when it rains!
Long length of ‘pavement’ on a slope, + bins of course
In this example there is a completely unnecessary ‘step’ between the pavment and driveway
Pedestrian Liberation 
Agree these are shocking, but aren’t they “pavement crossovers” for vehicle access to properties adjoining the road? I think of “dropped kerbs” as entirely beneficial to pedestrians. Their purpose is to facilitate the crossing of a road by the mobility impaired or those pushing buggies – useful and much appreciated by many especially as parking restrictions usually prohibit parking across a dropped kerb.
To a highway engineer and road law a ‘dropped kerb’ is exactly that – it is a place where the kerb is dropped to allow a vehicle to cross.
Here is an example for DirectGov: “A crossing across a public footpath or verge that allows your vehicle to gain access to your property from the highway is known as a ‘dropped kerb’ or vehicle crossing. Find out how to make an application for a dropped kerb or crossing.”
http://www.direct.gov.uk/en/HomeAndCommunity/WhereYouLive/StreetsParkingCleaningAndLighting/DG_10026223
And regarding enforcement: “The council provides a service for residents and businesses that find their dropped kerb (access to driveway) blocked by an inconsiderate motorist.”
http://www.hillingdon.gov.uk/index.jsp?articleid=7310