Lowest Percent of Population in The Capital - Europe

No, sorry, Londoner speaking - there's no sense in which inner London boroughs are regarded as 'city proper' and outer Londoners aren't. The Mayor of London has responsibility for all 32 boroughs plus the City of London. Nobody ever says 'London' and means 'City of London'. It always means the whole administrative metropolis. London's outer metropolitan area extends well beyond the city-region boundary.

The City of London is only around 6,000 people, though. There is no legal or administrative distinction between inner and outer boroughs, though. It's like New York - there's one bit (Manhattan) that's New York County, but all five boroughs are New York City. Or Berlin - it would be possible, but perverse, to say that only the borough of Mitte was 'city proper', not the whole city-region governed by the Mayor and Senate. The definition of London for all administrative purposes (surely the criterion for "city-proper") is the city-region governed by the Mayor of London.