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That's a problem but doesn't explain why the police in suburbia also don't live in London.
(For me most of zone 4+ is suburbia)
Police in London earn more than in the surrounding forces so there is an element of qualify with Hertfordshire Constabulary and then transfer to the Met and work in Barnet for a pay rise. I can understand why an individual would do that but it isn't policing by the community in my book.
There are some 2016 stats in https://www.london.gov.uk/sites/default/files/sian_berry_police_housing_report_jun2016.pdf - 7% living in borough is poor IMHO.
Issue there being they can't afford to live in the areas that they would want to I imagine, hence living in suburbia and then heading into work.