Halton was educated at Blencowe grammar school in Cumberland, became a student at Gray's Inn, and then entered the service of Thomas Howard, 23rd Earl of Arundel.
He transacted on his behalf affairs of importance in Holland, and on his return to England accepted and kept for twenty years the post of auditor of his household, involving duties connected with commissions and arbitrations.
Halton put up sundials at Wingfield Manor; and a letter written from Gray's Inn in May 1650, describing a dial of his own invention, was published in the appendix to Samuel Foster's Miscellanea, London, 1659.
Having heard of Flamsteed's astronomical proficiency, Halton called to see him at Derby in 1666, and afterwards sent him Giovanni Battista Riccioli's New Almagest, Johannes Kepler's Rudolphine Tables, and other books on astronomy.
A little later he speaks of observing with his quadrants, and on 27 December 1673 told Collins that 'lately, in discourse with Mr. Halton, he was pleased to show me a straight-lined projection for finding the hour by inspection, the sun's declination and height being given'.