Coote began his career as a youth at Alperton Old Boys, a team managed by the father of future England manager Ron Greenwood. He moved on to join Middlesex Senior League club Wembley as an amateur and impressed enough to spend two weeks on trial at First Division club Burnley in the spring of 1949.
Brentford
Ron Greenwood, then playing for Second Division club Brentford, knew of Coote and recommended to manager Jackie Gibbons that Brentford sign him. Coote joined the Bees as an amateur on 26 March 1949 and signed a professional contract on 9 May 1949. He made his debut for the club in a 4–1 defeat to Tottenham Hotspur at Griffin Park on the opening day of the 1949–50 season. He began his Brentford career as an inside left and scored his first goal for the club after 20 seconds of an eventual 4–1 defeat to Blackburn Roversin September 1949. Coote's Brentford career failed to ignite until player-managerTommy Lawton selected him as left half for a match versus Notts County in March 1953. Coote gave a strong performance in a 5–0 victory which eased the club's fears of relegation to the Third Division South. Coote became a near-ever present for Brentford and remained with the club after suffering relegation to the Third Division South in the 1953–54 season. Coote's durability over the next 9 years saw him claim the club record for consecutive FA Cup appearances and aside from playing on both flanks at full back, he also played in six other outfield positions. After missing the first 9 games of the 1954–55 season, Coote missed only 16 of the club's next 378 league games. Ever-increasingly used as a utility man, Coote filled eight different positions during his time at Griffin Park. Attention from First Division clubs Arsenal and West Bromwich Albion came his way, but deals never materialised. At the end of the 1960–61 season, Coote was jointly-awarded a testimonial with Johnny Rainford versus an All Star XI for his service to the club. Despite his durability, it was only during the 1962–63 season that Coote was an ever-present and he capped his campaign by captaining the Bees to the Fourth Division title. Coote made his final appearance in December 1963 and retired in April 1964, having made 559 appearances for Brentford. Coote's career virtually ran in parallel with goalkeeperGerry Cakebread and both players were named on the teamsheet together 357 times. He remains the club's record appearance-maker and was never booked in his career. Coote was offered opportunities to continue his career in non-League football, but chose to remain in retirement. He was awarded a second testimonial versus West Ham United, managed by Ron Greenwood, in September 1965, from which he earned more than £1,000.
After completing his National Service and before signing for Brentford, Coote worked for his father in removals. After retiring from football, Coote used the £1,000 earned from his second testimonial match to buy a three-bedroom semi-detached house in the Brentford area. He later became manager of a betting shop in Hounslow, owned by former Brentford teammate Frank Morrad. On 2 August 2003, Coote died aged 75 following a short illness. He had been living in Whitton.
