When the LCC (London County Council) was formed in 1887 - it took in areas of - Kent and Surrey - a very small part of Essex - and the total administration for Middlesex - (The county of Middlesex ceased to exist in all but name). For example - instances of Depford, Greenwich, Lewisham, Plumstead and Woolwich will appear in both Kent and London depending upon the date of the event. The London Metropolitan Archive may be regarded as the equivalent to a County Record Office for Middlesex - although this library covers a lot more than just Middlesex.
Generally - records have remained with the original counties with the exception of Middlesex.
The administrative area of London was further increased in 1964 when the LCC was replaced by the GLC (Greater London Council). However the GLC was short lived as it was abolished in 1986 and its powers devolved to the London Boroughs.
The definition of a London Home County - is a county that has a common boundary with London. These counties are Essex, Kent, Middlesex and Surrey.