He was educated at Rugby School and Balliol College, Oxford, from which he earned a bachelor"s degree in 1772.
Their daughter, Julia Evelyn Medley Shuckburgh, married Charles Jenkinson, 3rd Earl of Liverpool. Shuckburgh died on 11 August 1804 in Shuckburgh, Warwickshire. He made a series of astronomical observations and an ephemeris, which he published in twelve volumes between 1774 and 1797.
In 1791 the Shuckburgh telescope was installed at his private observatory in Warwickshire, England.
Included among his observations were measurements of lunar surface features. The crater Shuckburgh on the Moon is named after him.
Shuckburgh also contributed to metrology. He performed a series of observations on the change in the boiling point of water at different pressures, and pointed out the need for controlling for this effect when calibrating thermometers.
The Shuckburgh scale was a standard brass yard constructed for him by Edward Troughton, whose company later made the Victorian standard yard of 1855.
The Shuckburgh scale was used by George Biddell Airy in his measurements of the earth"s shape, and in setting standards for many years by the British government. In statistics, Shuckburgh was a pioneer in the collation of price indexes. He became a Fellow of the Royal Society in 1774.
Royal Society; 1st United Kingdom Parliament. 2nd United Kingdom Parliament]
He served in the House of Commons as a Member of Parliament for Warwickshire from 1780 until his death in 1804.