I was thinking of something like the following admittingly amateurish examples of 4 Main Underground Lines that avoid Central London and allow the potential for other existing Underground Lines or smaller alternate Undergrounds to cover the remaining areas, where the Underground is currently not present and making for a more integrated and wider reaching London Underground network with people being more inclined to use public transport.
Northeast to Northwest London - Woodford (Central) to Moor Park (Metropolitan) via the areas (Not Stations) of Chingford, Enfield, High Barnet, Borehamwood or Radlett and Bushey where the Underground currently does not extend to.
South to Outer East London - West Croydon (Overground) to Harold Hill via the areas (Not Stations) of New Arlington, Orpington, Swanley, Dartford, Purfleet, Rainham and Romford.
Northwest to Southwest London - Moor Park (Metropolitan) to Epsom (proposed Crossrail 2 station) via the areas (Not Stations) of Harefield, Denham, Uxbridge, Hillingdon, Hayes, West Drayton, Hounslow, Twickenham, Teddington, Kingston upon Thames, Surbiton and Chessington.
Southwest to Inner East London - Dagenham Dock (proposed DLR station) to Epsom via the areas (Not Stations) of Belvedere, Bexleyheath, Sidcup, Chislehurst, Bromley, West Wickham, South Croydon, Purley and Banstead.
At the Moment if someone wanted to go from Woodford to say High Barnet for example they would have to journey via Central London on the Central and Northern Lines, putting up with long journey times and overcrowding at rush hour when the Woodford-Moor Park Line would potentially cut journey times by about 50 mins to an hour and greatly ease overcrowding during rush hour.