As a child, Jonny spent time playing and training at Royal Wootton Bassett Rugby Football Club in their Mini & Junior teams. After joining Gloucester’s rugby academy, he made his first start for Gloucester Rugby in a pre-season friendly against Bath Rugby on 15 August 2009, and the next weekend he scored a try against Connacht after he had come off the bench. His first taste of first team action came in the Heineken Cup when he replaced Charlie Sharples against Newport Gwent Dragons and just over a month later he made his first start against London Wasps in the Anglo-Welsh Cup,playing on the wing. On 20 February 2010, May was a late replacement for Gloucester’s match against Leicester Tigers at Welford Road Stadium after Fuimaono-Sapolu pulled out with a dead leg. Although Gloucester lost, May played well and scored a try on his Premiership debut. May made 2 more starts for Gloucester during the remainder of the season against London Wasps and Northampton Saints.

In January 2012 May was called up to the England Saxons, which he celebrated by scoring two tries from full-back for at Kingsholm against Toulouse in the Heineken Cup. May made his debut off the bench against Scotland, and made his first start against Ireland the following week. In March 2012 May was named as the inaugural winner of the LV= Breakthrough Player Award. May was named Gloucester’s Young Player-of-the-Year for 2011/2012, and his stunning solo effort against Harlequins was named Try-of-the-Season at the Aviva Premiership Awards. In December 2012, May signed a two-year contract extension with Gloucester until the end of the 2014–15 season. On 24 October 2014, May signed a new long-term contract with Gloucester Rugby.

May was called up to the senior England tour of South Africa in June 2012, scoring two tries in England’s 57–31 win over Sharks. May won his first international cap during England’s 2013 summer Tour against Argentina in the second Test which England won 51–26. On 9 January 2014, May was called up for the 2014 Six Nations Championships where he was in the starting fifteen against France, Scotland, Ireland, Wales and Italy. He started the first test against the All Blacks in England’s 20–15 defeat, but was dropped for the next two tests.

In 2017 it was announced he would be joining Leicester Tigers in a swap deal with Ed Slater, after activating a little known clause in his Gloucester contract. May started his Leicester career strongly scoring 9 tries in his first 8 appearances and earning the club’s player of the month award.

After three seasons at Welford Road, in April 2020 it was announced that May would return to Kingsholm for a second stint. He has since agreed a long-term contract.