Hi
The double taxation agreement between the UK and the USA at article 17(3) advises that payment made by the USA for social security or similar to a resident of the UK, shall be taxable only in the UK.
Please see
UK/USA DOUBLE TAXATION CONVENTION
Pensions paid by the US government to members of the US armed forces, or to their surviving spouses or children) in respect of their period of service continue to be regarded as paid for services rendered to the United States.
Such pensions therefore come within Article 19 (Government Service) of the convention and are exempt from UK tax unless, exceptionally, the recipient is both a national and a resident of the UK in which case the pension is taxable only in the UK. Take a look at the guidance here
DT19853 - Double Taxation Relief Manual: Guidance by country: United States of America: Notes
You are free to work in the UK when in recipt of this pension.
Thank you