The Department does not record the number of veterans who reside in each local authority.
An estimated distribution of the UK Armed Forces veteran population residing in Great Britain can be found in the 'Annual Population Survey: UK Armed Forces Veterans Residing in Great Britain', the latest edition of which (2017) is published at: https://www.gov.uk/government/collections/annual-population-survey-uk-armed-forces-veterans-residing-in-great-britain. As at 2017, there were an estimated 2.4 million UK Armed Forces veterans residing in households across Great Britain.
The sample size of the Annual Population Survey is statistically too small to produce veteran estimates at geographical locations below county level.
However, the Department does hold information on UK Armed Forces veterans in each local authority who are in receipt of an Armed Forces occupational pension, a disablement pension under the War Pensions Scheme or compensation under the Armed Forces Compensation Scheme. This information can be found in table 3 of “Location of Armed Forces pension and compensation recipients: as at 31 March 2018 (annex A)” which is published at: https://www.gov.uk/government/statistics/location-of-armed-forces-pension-and-compensation-recipients-2018.