In 1751 Mudge set himself up in business at 151 Fleet Street, and began to advertise for work. He rapidly acquired a reputation as one of England’s outstanding clockmakers. In 1753 he married Abigail Hopkins of Oxford, with whom he had two sons.
Around 1757, he invented the lever escapement, which was the greatest single improvement ever applied to pocket watches, and remained a major feature of every pocket timekeeper for the next 200 years.
In 1765 he published ‘Thoughts on the Means of Improving Watches, Particularly those for Use at Sea’.
In 1771, due to ill-health Mudge, quit active business and left London to live in Plymouth. From that date Mudge worked on the development of a marine chronometer that would satisfy the rigorous requirements of the Board of Longitude. He sent the first of these for trial in 1774, and was awarded 500 guineas for his design. He completed two others in 1779 in an attempt to gain one of the higher awards. They were tested by the Astronomer Royal, Nevil Maskelyne, and declared as being unsatisfactory. There followed a controversy in which it was claimed that Maskelyne had not given them a fair trial. A similar controversy had arisen when John Harrison had been denied his prize by Maskelyne. Eventually, in 1792, two years before his death, Mudge was awarded £2,500 by a Committee of the House of Commons. In 1770 George III purchased a gold watch produced by Mudge, including his lever escapement. This he presented to his wife, Queen Charlotte, and it still remains in the Royal Collection. In 1776 Mudge was appointed watchmaker to the king.