Fenwick began his youth career at Crystal Palace where he was part of the successful team that won the F.A. Youth Cup in both 1977 and 1978, scoring the only goal in each final in two 1-0 wins over Everton and Aston Villa respectively. He signed professional terms with Palace, in December 1976, made his league debut away to Tottenham Hotspur in December 1977 and went on to make 10 appearances that season. The next season (1978–9) Palace were promoted to the top flight and Fenwick made a further 20 appearances and 10 in 1979–80 in the old Division One. During those three seasons, Fenwick wore eight different numbered shirts for Palace at a time when shirt numbers equated more to playing position. Fenwick started the next season as first choice left back after the departure of Kenny Sansom, but after a poor start to the season the club looked set for relegation and in December 1980, Fenwick rejoined former Palace manager Terry Venables at Queens Park Rangers. He had made 70 league appearances for Palace, but without scoring.
Fenwick signed for Queens Park Rangers in December 1980 for £110,000 and went on to make 256 appearances scoring 33 goals. Whilst at Queens Park Rangers, Fenwick made his debut for the full England side, in May 1984 as a substitute for Alvin Martin, at Wrexham. He also became the first full back to score a goal from open play in an FA Cup Final when he equalized against Tottenham Hotspur in the 1982 final.
In December 1987, Fenwick was again signed by Terry Venables for Tottenham Hotspur, for a fee of £550,000 and went on to make 93 appearances for Spurs, scoring eight times all from the penalty spot in just one season, 1988–9. In 1990–91 Fenwick had a loan spell at Leicester city (eight appearances 1 goal) and in 1993 moved on to Swindon Town.
In 1993 Fenwick signed for Swindon Town, at that time a newly promoted Premier League team.His first season, 1993–4, saw Swindon winning only 5 games of a total 42, conceding 100 goals and being relegated. Fenwick played 28 games during this season, and was noted for involvement in an incident which resulted in a broken leg for Paul Warhurst. He played only two games the following season, was released, and ended his playing career shortly thereafter.
Fenwick made his international debut for the full England side in May 1984 as a substitute for Alvin Martin at Wrexham, and went on to make 20 appearances for the national side up until 1988.
He holds the English record for most yellow cards, three, in a single World Cup tournament, which he achieved in the 1986 FIFA World Cup. During that World Cup, Fenwick was also noted for being passed by Diego Maradona as Maradona scored the "Goal of the Century".
Fenwick received a four-month prison sentence in September 1991 after being convicted of drink-driving. He served two months of his sentence.
Fenwick married Reyna Kowlessar, a Trinidadian lawyer in January 2014.
Following in the footsteps of many former players, Fenwick decided to try a managerial career. In 1995, he replaced Jim Smith as manager for Portsmouth. After an underwhelming first full season in charge, where the club only avoided relegation on goal difference, an improved second season saw the club miss out on a play-off spot by just one place, and they also eliminated then-Premier League Leeds United from the FA Cup. A dire third season cost Fenwick his job however, and he left with the Club bottom of the Division One table.
In a quite remarkable turnaround of events, Fenwick was canvassed by an Asian businessman and coerced to become the new public face of beleaguered non-league outfit Southall between 2000-2001. It led to fellow Queens Park Rangers teammate Mike Fillery being installed to take charge of first team affairs, before both were ousted amid the debacle surrounding the Club's ownership.
Fenwick's next manager job was at Northampton Town in 2003, where he only lasted for 7 games. His first game saw a 1–0 lead turn into a 2–1 defeat away to Blackpool. The next five games saw just two draws and three more defeats. His last game in charge was against Bristol City. The 2–1 defeat saw calls for his departure from fans and he left the post the following Monday. He was replaced by Martin Wilkinson. That summer, Fenwick was lined up to become the new manager of Luton Town, but he decided not to take the job due to uncertainty over the Club's ownership - amid allegations of fraud surrounding Hatters, and former Southall chairman John Gurney.
After enduring a fairly torrid time with Southall, through no fault of his own, in 2004, Fenwick became director of football at Isthmian League side Ashford Town. Yet, despite plans to reshape the Club for bigger things, a lack of private investment and on-field success, meant the Club was unable to move forward.
Since his managerial days in England, Fenwick has spent a considerable amount of time in Trinidad and Tobago, where he has enjoyed a great degree of managerial success - winning the country's professional football league on four occasions (2002, 2003, 2007, and 2008). After securing a place in the Caribbean Champions League for Central FC, Fenwick signed for CS Visé in the Belgian Second Division at the time of the signature but the club was relegated at the end of the season.