Born in Beverley, Humberside, Stamp grew up in Hessle, playing football from an early age for his local side Hessle Rangers. It was while playing for this club that Stamp was spotted by the manager of Pontefract Collieries. He signed for the West Yorkshire side and played only a handful of games before departing to play as a professional.
Scunthorpe United
Stamp joined Scunthorpe United. Stamp signed a professional contract with the club at 17 yearsof age. Although he was keen to pursue his dream to be a professional footballer, he also continued his studies and stayed on at Hessle College to do A Levels in English Literature, Geography and P.E. He took part in the 1999 play-off final, when Scunthorpe United beat Leyton Orient 1–0. After four seasons at Scunthorpe, playing regularly in the reserve team and also making thirty starts for the first team, Stamp was transferred to Scarborough. Scarborough reported Northampton Town to the Football Association, after they made an alleged illegal approach for Stamp.
Northampton Town
He spent a year at the club and scored 14 goals before joining Northampton Town for £50,000. During his time at Northampton there was a lot of upheaval at the club. In the space of just over a season there were three different managers and three different chairmen, with players being transferred at an alarming rate.
Chester City
Stamp too was soon on the transfer list and was sold to Chester City for £15,000 in August 2003. He scored 20 goals during the 2003–04 season and helping to secure promotion for the club back into the Football League. He struck up a prolific partnership with Daryl Clare, with the pair scoring nearly 50 goals between them during that season. Chester sealed their promotion during the last home game of the season when they were playing Scarborough. Stamp scored the winner against his former club, securing Chester's status as Football Conference champions. He rejected a loan move to Forest Green Rovers in October 2004. After struggling to regain his place in the Chester side following the arrival of new manager Ian Rush, playing just five games under him and failing to score.
Stevenage Borough
Stamp was transferred to Stevenage Borough during the 2004–05 season. He played in the 2005 Conference National play-off Final where Stevenage missed out on promotion to Carlisle United. Despite scoring 14 goals in the 2005–06 season, Stamp felt he had fallen out of favour at the club due to the appointment of new manager, Mark Stimson. He signed a new contract with Stevenage in May 2006.
York City and Halifax Town
He joined York City on a three-month loan deal in the 2006–07 season. He joined Halifax Town in January 2007, in a deal which runs until June 2008. He joined Northwich Victoria on loan until the end of the 2007–08 season in March 2008. He made his debut in a 3–1 victory against Droylsden. He was recalled back to Halifax in April to help the club's battle with relegation. His return had an immediate effect after scoring after coming on as a substitute in the game against Forest Green on 5 April 2008. He was transfer-listed by the club after their demotion from the Conference Premier.
Stamp re-signed for Victoria on a permanent deal, but would depart the club after playing 26 games, scoring 6 goals. On 26 March 2009, Stamp joined Conference North side Gateshead on loan until the end of the season. He made his debut two days later against Hinckley United, scoring the fourth goal in a 5–0 victory. Stamp signed for Gainsborough Trinity on 9 June 2009. After one season with Trinity he was released.
Guiseley and return to Gainsborough
Stamp joined Guiseley in July 2010, and went on to be a part of the side that eventually lost in the Conference North play-offs. Stamp re-joined Trinity in June 2011. He notably scored the equaliser in Trinity's televised 3-1 FA Trophy semi-final first leg defeat away against Wrexham. He was released at the end of the 2015–16 season.
