He was then elected as MP for Glasgow Queen's Park, and held that seat until he suffered a heart attack  and died in office in 1982 at the age of 53, while participating in a 'Day of Action' march and demonstration in support of National Health Service workers in Glasgow. He served as Parliamentary Under-Secretary of State for Scotland from 1975 to 1979.
Their son is the musician Johnny McElhone.
- "Mr Frank McElhone (obituary)". The Times. 24 September 1982. p. 11.
- Times Guide to the House of Commons, 1979
- Leigh Rayment's Historical List of MPs [self-published source][better source needed]
|Parliament of the United Kingdom|
|Member of Parliament for Glasgow Gorbals
|New constituency||Member of Parliament for Glasgow Queen's Park
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