He was son of Robert Peachell or Pechell of Fillingham, Lincolnshire, was educated at Gainsborough school, and was admitted as a sizar of Magdalene on 1 August 1645.
In 1661 Samuel Pepys spent an evening with him at the Rose tavern in Cambridge; but he says objected to be seen walking with Peachell on account of his drinker’s nose.
In the course of 1686 James II discovered that John Lightfoot had not taken the oaths required under the Test Act when he was admitted to his master's degree at Cambridge, and he furnished with royal letters patent a Roman Catholic candidate for the degree, the Benedictine monk Alban Francis.
Peachell wrote to the Duke of Albemarle, who was then chancellor of the university, and also to the Earl of Sunderland, to beg their intercession with the king.
On 9 April a summons was sent down citing the vice-chancellor and deputies of the senate (among them Isaac Newton) to appear before the Ecclesiastical Commission.
Peachell did not long survive as Master; during a visit to Cambridge in 1690 the Archbishop of Canterbury William Sancroft rebuked him for drunkenness and ill-conduct.