Mundee began his career in youth football in Swindon and represented the town's schoolboy team. Mundee was offered a two-year apprenticeship deal worth £5,000 by Harry Redknapp, but he instead decided to sign for top-flight club Queens Park Rangers. Mundee's father kept the details of the Bournemouth transfer fee secret from his son, to help the young Mundee make a decision based on which club felt best for him and not influenced by money. Mundee failed to make a first team appearance for Rangers and moved to hometown Third Division club Swindon Town in August 1986, turning professional. He again failed to make an appearance and after his release, he dropped into non-League football and jooned Southern League Premier Division club Salisbury.
Mundee signed for Second Division club Brentford on non-contract terms on 12 August 1993. He had been a transfer target of former manager Phil Holder during the 1992–93 season, but the move broke down. Mundee began life at Griffin Park under David Webb as a right back, filling in for the injured Brian Statham. After a training ground bust-up between Mickey Bennett and Joe Allon, Mundee was moved up front. The high-point of Mundee's Brentford career came in a home match against Bristol Rovers in January 1994, in which he scored a hat-trick in a 4–3 defeat. He finished the 1993–94 season as Brentford's second-leading goalscorer, with 13 goals. Now behind the 'FT Index' in the pecking order up front, Mundee was a regular off the bench in the first half of the 1994–95 season, before finally breaking into the starting line-up in November 1994. He made 45 appearances and scored five goals during a frustrating season, in which the Bees finished second in the Second Division, only to be forced to settle for a play-off place due to the reduction in size of the Premier League and its effect on the league pyramid. Brentford lost on penalties to Huddersfield Town in the semi-finals, with Mundee missing his spot kick in the second leg. Mundee's relationship with manager David Webb soured during the 1995 off-season. While negotiating a new contract, Mundee requested a £5,000 signing-on fee, which would enable him to replace his car, in which he was driving 200 miles a day, commuting to Middlesex from his Bournemouth home. Mundee was given a week-to-week contract and was released in October 1995, with the chairman citing budgetary concerns. Mundee became disillusioned with football, as Webb had insinuated in the local press that Mundee had been living an expensive lifestyle, when in reality his wages were £450 a week. Mundee made 100 appearances and scored 18 goals in just over two years at Griffin Park. Looking back in 2005, Mundee said "I can honestly say that the time I spent at Brentford means more to me than any other club I have been at".
Mundee moved to Second Division club Brighton & Hove Albion on a one-month contract on 19 October 1995. The man who signed Mundee, Liam Brady, was soon sacked and Mundee's future was assured when former Bournemouth teammate Jimmy Case was appointed manager. Mundee made 62 appearances and scored eight goals during a terrible period for the Seagulls, which had seen the club plummet to the bottom of the Football League by the time he was released on 11 December 1997. Back and ankle injuries and weight gain brought about the end of his professional career.
Mundee attempted to resurrect his career by joining Southern League Premier Division club Dorchester Town in late 1997. However, with his contract still held by Brighton & Hove Albion, he was twice listed for his Dorchester Town debut, but was unable to play.
Non-league football
Mundee ended his career with a number of short spells in non-league football during the second half of the 1997–98 season, with a return to Salisbury City and short spells with Newport, Swindon Supermarine, Clevedon Town and Bath City.
Personal life
Mundee grew up in Swindon, to parents from Shepherd's Bush, London. His brothers Barry and Brian also became footballers, with Brian playing league football for Bournemouth, Northampton Town and Cambridge United. As of 2005, Mundee was working as a self-employed exterior wall coating specialist, alongside his brother Brian.