Gascoyne grew up in Norfolk, attending Wymondham College from 1974 to 1981. He began doctoral research in fluid dynamics at Churchill College, Cambridge, from 1982, accumulating degrees but leaving without completing his PhD in 1988. A committed Cambridge Boat Club coxswain alongside his academic work, he joined Westland System Assessment briefly before moving into motorsport.
In 1989 he joined McLaren as a wind tunnel aerodynamicist but moved after a year to Tyrrell, where he worked under designer Harvey Postlethwaite. When Postlethwaite left in 1991 to design Sauber's first Formula One car, he brought Gascoyne to Switzerland with him. Gascoyne remained with Sauber through the 1993 season, during which the Sauber C13 scored 12 championship points on its Formula One debut.
Postlethwaite returned to Tyrrell in late 1993 and invited Gascoyne to become deputy technical director. Gascoyne spent four years at Tyrrell but limited funding constrained what the team could achieve. When Ken Tyrrell sold the outfit to British American Tobacco and the renamed British American Racing engaged Malcolm Oastler as technical director, Gascoyne moved on.
In June 1998 Gascoyne joined Jordan Grand Prix as technical director, succeeding Gary Anderson. The 1999 season proved the most successful in Jordan's history: the team finished third in the Constructors Championship and took two race victories with Heinz-Harald Frentzen.
Shortly before the 2001 season Gascoyne moved to Benetton, a team in steep decline since its mid-1990s championship years. His technical stewardship over two and a half seasons, spanning the rebranding as Renault F1, culminated in a victory at the 2003 Hungarian Grand Prix. Before the season concluded, however, Renault placed him on gardening leave in anticipation of his departure to Toyota, settling the matter for an undisclosed fee.
Gascoyne joined Toyota's Cologne base in December 2003. The 2004 season was difficult, with Gascoyne having had insufficient time to influence the car's design. The 2005 campaign was Toyota's strongest in Formula One, with points in nearly every race and Jarno Trulli taking pole position at the United States Grand Prix — though like all Michelin-shod runners, Toyota did not start the race. With expectations high for 2006, Toyota dismissed Gascoyne after two races, citing a "fundamental difference of opinion" over technical direction. Ralf Schumacher had finished third on the podium in Melbourne, making the dismissal particularly surprising to outside observers.
In September 2006 Gascoyne joined Spyker F1 as chief technology officer. He introduced an updated F8-VII chassis at the 2007 Turkish Grand Prix, the first car bearing his design input at the team. When Vijay Mallya acquired the outfit and rebranded it Force India in 2008, Gascoyne continued in the CTO role until November 2008, when Mallya restructured the technical leadership.
From 2009, Gascoyne was the driving engineering force behind the revived Team Lotus entry for 2010, working with Malaysian government backing under the Lotus Racing brand. Through successive name changes the team raced as Team Lotus and then Caterham F1, with Gascoyne extending his contract to 2015. From 2012 he stepped back from the F1 operation to lead Caterham Technology and Caterham Composites as CEO, applying Formula One engineering and project management methods to automotive, marine, and aviation applications.
Gascoyne founded MGI Engineering (originally MGI Motorsport) in 2003, based in Oxfordshire, specialising in lightweight composite solutions for motorsport, aerospace, automotive, and marine sectors, with increasing focus on electric vehicle and eVTOL aircraft development.
He also competed in offshore sailing, completing a solo non-stop transatlantic crossing in 2012 aboard a Class 40 racing yacht, and co-skippered a campaign under the Caterham Challenge banner that finished third in the 2015 Rolex Fastnet Race.
Gascoyne's career produced competitive results at nearly every stop — Jordan's 1999 season, Renault's first post-Benetton win, Toyota's strongest campaign — yet recurring friction with team management truncated each tenure before longer-term projects could fully mature. His willingness to move between drastically different team cultures, combined with a reputation for technical rigour and forthright opinions, made him one of the most distinctive engineering personalities of Formula One's 2000s era.