I would have thought initially most drivers would respond to the signs,
if only to cut their speed from a margin under 40mph to a margin under 30mph. But that is better than nothing.

Lewisham are not acting alone, as Southwark are making the change, Islington have made it, and 30Km/h limits are becoming common in residential areas in France, Germany, Belgium, Austria, Netherlands, Sweden, Norway and Switzerland.
This new limit is not going away.

Once the limit becomes more widespread, tfl need to run hard hitting tv/radio/newspaper campaigns to educate drivers why this is so important, just like the drink driving campaigns of the 70s.

Once public opinion is fully behind the new limit, the courts can hopefully take some measures to deter those who do not get the message.