You asked
Please provide a breakdown of each and every airport in the UK by region.
We said
Thank you for your request.
Unfortunately we do not maintain a list of all airports in the UK.
We do maintain and publish a set of NUTS 1 boundaries under open data license terms and they can be downloaded in a range of common formats and at no charge here:
http://geoportal.statistics.gov.uk/datasets/nuts-level-1-january-2015-boundaries
For a list of all UK airports we would direct you to the Civil Aviation Authority or to Ordnance Survey.
Based on its address, Gatwick Airport is located in the South East NUTS 1 Region but allocated to the London NUTS Region for the Country and Regional Public Sector Finances, as explained in response to an earlier FOI which you raised: