Parkin was born on 27 October 1829 at Cowley Manor in Ecclesfield in the West Riding of Yorkshire, now a part of Sheffield.

He was the son of John Jeffcock J.P. (1803–78) and his wife Catherine (1804–72, née Parkin) Lady of the Manor of Darley.

[1] In 1861, his bravery was noted when he attempted to rescue the men and boys trapped in a coal-pit at Clay Cross during an inundation.

With three others, including Mr Smith, an engineer and David Tewart, the steward of the colliery,[7] he descended to make an exploration of the workings.

The sole survivor was rescued on 14 December 1866 by Thomas William Embleton and John Edward Mannatt.

[1] A (c. 4.5 m) memorial on Doncaster Road in Barnsley was built in 1913 to commemorate the bravery and sacrifice of Jeffcock and the other rescuers.