Charlton was educated at Magdalen College, Oxford and admitted to Lincoln's Inn in 1633.
He was Member of Parliament for Ludlow and was briefly Speaker of the House of Commons in 1673.
His son, the second Baronet, was Member of Parliament for Ludlow and later Bishops Castle and was high sheriff of Shropshire in 1698.
The Baronetcy was extinct on the death of the fourth Baronet and the Shropshire estate passed to his nephew Nicholas Lechmere Charlton.
The public house in Ludford (the Charlton Arms) is named after the baronets.