In 2006, he switched from swimming to cycling, competing at international events in the
C4 disability category. Winning gold in the kilo in his debut at the 2006 world championships, he repeated this feat in 2007 and 2009 also taking the team sprint title at both events.
Representing Great Britain at the
2008 Summer Paralympics in
Beijing, Cundy broke the world record on the way to winning the gold in the
1km Time Trial with a time of 1 minute 5.466 seconds. He was selected for the Great Britain team at the
2012 Summer Paralympics. He was expected to win gold in the C4/5 Men's 1 km time trial, but slipped shortly after starting, which he argued was due to the starting gate not working properly. The technical delegate of the International Cycling Union, Louis Barbeau, disagreed, refusing him a restart. Cundy then erupted into a rage, swearing and throwing water bottles. He later apologised to the crowd, though made clear that he still disagreed with the decision. He won bronze in the C4 men's 4 km pursuit, racing
Diego Gomez of
Colombia. In the first kilometre of the race, he clocked a time of 1:05.317 in the heats, which would have won the 1 km time trial. Cundy aimed to qualify for the England team for the
2014 Commonwealth Games, but he abandoned this hope after placing fifth among English competitors and eighth overall in the
1km time trial at the 2013
British National Track Championships, despite setting a new personal best and a world record for the
C4 category. Subsequently, he won gold at the 2014
UCI Para-cycling Track World Championships in
Aguascalientes in the C4 1 km time trial, earning his ninth world title and breaking his own world record with a time of 1:01.466. In 2015 and 2016, Cundy remained undefeated in the 1 km TT. In addition to his 2016 Kilo Gold Medal, he became a double world champion with British Cycling teams mates
Louis Rolfe and
Jon-Allan Butterworth winning in a new world record time at the
World Championships in Montichari, Italy in March. At the
2016 Summer Paralympics in Rio, Cundy regained his Kilo Paralympic title in a new Paralympic record of 1:04.492 which when factored for C4 athletes gave a winning time of 1:02.473 In the final track cycling event of the
2016 Summer Paralympics Cundy teamed up with Louis Rolfe and Jon-Allan Butterworth to take the Mixed Team Sprint C1-5 gold medal in a world-record time of 48.635. Cundy was appointed
Member of the Order of the British Empire (MBE) in the
2009 New Year Honours for services to disabled sport, and
Officer of the Order of the British Empire (OBE) in the
2017 New Year Honours for services to cycling and swimming. At the 2020 Paralympic games in Tokyo, he took home the Silver in the C4-5 1 km Time Trial behind Spanish C5 Athlete
Alfonso Cabello. Two days later he teamed up with
Kadeena Cox and
Jaco van Gass to take Gold, in a new WR time of, 47.579 in the C1-5 Mixed 750m Team Sprint ahead of the current world champions China. In winning his silver medal at the Tokyo Paralmypics he became the first male Great British athlete to medal at 7 consecutive Paralympic Games. Cundy was appointed
Commander of the Order of the British Empire (CBE) in the
2022 New Year Honours for services to cycling. ==Television==