I am referring to this graph. I did check the article (where I found the exact years of decline) and a few others it linked to but, strangely, I couldn't find an explanation.
http://en.wikipedia.org/wiki/File:Population_greater-london_graph.gif
I would speculate that it was a result of a number of factors ie. improved transport networks making commuting a more feasible option for many professionals. Milton Keynes, for example, was built specifically to accommodate skilled professionals working in London, Oxford and Birmingham. The town began construction in the late 1960s, with population growth dramatically outstripping the rest of the UK.
Add this to additional factors such as rising property prices, climbing population density and the rise of council accommodation, a pattern begins to emerge. The recent rise of London's population can likely be attributed to a mixture of high-density urban developments, the growth of technology-assisted professions that requires less working space, and the general increase in London's wealth.