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The department publishes figures on the number of independent schools and pupils attending them in the annual ‘Schools, Pupils and Characteristics’ release, by national totals and by local authority in tables 1a, 1b, and 1c, available here:
The underlying data file includes figures for individual schools including school name, school type, parliamentary constituency and location. Full addresses can be found at the Get Information About Schools website, available here: https://get-information-schools.service.gov.uk/.
The Oxford Analytics October 2018 report, 'The Impact of Independent Schools on the UK Economy' estimated that independent schools provide an annualised taxpayer cost saving of £3.5 billion, compared to the cost of educating all pupils in the state sector.