Err, you are also inaccurate, flierfy, while correcting the "the whole southern England uses third rail" inaccurate statement.
1)Parts of the North London Line (west of Acton Central, Camden Road - Stratford (though trains now use OHLE from Dalston eastwards) and West London line (from not far south of Willesden Junction southwards) are 3rd rail electrified and north of the Thames, likewise the ELL and Watford DC lines. All these lines are part of the London Overground network for those that don't know.
2)Parts of the South West Trains network is north of the Thames and 3rd rail electrified - bridges just west of Richmond, between Staines and Egham, Datchet and Windsor, Kingston and Hampton Wick and Barnes Bridge. 24 stations in all north of the Thames.
3)The London Underground uses 4th rail electrification (though the 3rd rail is also electrified).
Therefore, it is not only the lines south of Thames, nor London Underground using 3rd rail </pedant>
What Coccodrillo ought to have said is that most of the old Southern Region still in passenger service uses 3rd rail (Uckfield branch, Ore-Ashford and Basingstoke-Exeter-beyond being the exceptions). This would exclude the London Overground lines with 3rd rail electrification, but would be correct. It's also worth pointing out that, while all the network would be used by commuters (and not just London ones), a lot of it isn't "commuter rail".
Also, Merseyrail (Liverpool area commuter network) uses 3rd Rail electrification on the Northern and Wirral lines.