Hi. For a USC, a government (state, local, county/parish, federal, school board, etc.) pension is taxable in the USA and not the UK. US Social Security pension payments are only taxable in the UK. Both per the US/UK tax treaty. Note section (b) for the "except when" clause.
And from the tax treaty:
(a) any pension paid by, or out of funds created by, a Contracting State
or a political subdivision or a local authority thereof to an individual in respect
of services rendered to that State or subdivision or authority shall, subject to
the provisions of sub-paragraph b) of this paragraph, be taxable only in that
State;
(b) such pension, however, shall be taxable only in the other
Contracting State if the individual is a resident of, and a national of, that State.