Richard Martyn's birth is estimated at c. 1534 on the basis of his age given as 28 in a portrait medallion by Steven van Herwijk dated 1562. He was elected a liveryman of the Worshipful Company of Goldsmiths, one of the Livery Companies or craft guilds of the City of London, in 1558. He was elected alderman for the wards of Farringdon Within 1578–1598 and Bread Street 1598–1602. He was Sheriff of London in 1581–1582. Martin was knighted in 1588–1589 and served a partial year as Lord Mayor in 1589, succeeding Sir Martin Calthrop who had died in office. He was Prime Warden or head of the Goldsmiths' Company 1592–1593, chairing the Court of Wardens or governing body of the company, and served a second term as Lord Mayor in 1593–1594, succeeding Sir Cuthbert Buckell. His other municipal offices included President of Christ's Hospital and Comptroller-General of Hospitals 1594–1602. Martin was Warden of the Royal Mint by 1572, and was responsible for overseeing the workings of the mint and the quality of the coinage. John Stow's Survey of London records Martin's charges against John Lonyson or Lonison, Master of the Mint, in the 1570s, a matter that was finally weighed by a commission of Privy Council members including Nicholas Bacon, the Lord Keeper, William Cecil, Lord Burghley, the Lord Treasurer, and others, which recommended that Martin himself succeeded Lonyson as Master of the Mint in 1582, serving in that capacity until his death in 1617. He provided silver plate for the use of Mary, Queen of Scots, including a silver gilt bowl and cover in 1585, decorated with an engraved pattern of fish. Martin was an investor in Sir Francis Drake's 1577–1580 voyage of circumnavigation and also in Drake's 1585–1586 expedition to harass the Spanish ports in the New World. In 1589 Martin supplied silver plate, silks, and other goods to the value of £2,000 which Elizabeth gave to James VI of Scotland for the reception of Anne of Denmark. James VI took some of this silver plate to Oslo and presented it to the Danish councillor Steen Brahe.
Martin had remained both Warden and Master of the Mint for almost two decades, but following charges in 1597 that he was profiteering by delaying repayments he sold his office of Warden to Sir Thomas Knyvet. The two soon fell out, with Knyvet accusing Martin of owing the crown substantial funds and Martin insisting he was owed. Martin was briefly imprisoned for debt, which led to his removal from his Aldermanry on 31 August 1602 on account of his "unfitting demeanour and carriage". Suits and countersuits continued, with the Exchequer finding against Martin in 1607 and a further enquiry finding in his favour in 1615. He died in July 1617, and was buried in Tottenham Church, 30 July 1617. At his death he "was held near a hundred years old". His wife Dorcas had been buried in the same church on 2 September 1599, and his son Richard on 28 May 1616.
