The definition of London and Greater London used by the London Technology Fund is the 32 boroughs and the City of London. The geographic boundary is illustrated in this map. You can check whether you are in London using this postcode checker: http://www.gigateway.org.uk/areasearch/default.html
As Greater London has expanded, parts of the counties of Middlesex (to the North) and Surrey (to the South) are now included in London. Old birth certificates may refer to "Southwark, Surrey" and "City Road, Middlesex" but these are now well within the Greater London area and, in particular, the Underground network.