A small, but lively striker, who scored his fair share of goals, but was perhaps a little lacking in height to make it at the very top level, although he had a good spell with Norwich City and made the Northern Ireland national team at the peak of his career, despite being in the Tottenham reserve side at the time.
Having come over from Northern Ireland, where he had represented Belfast Schools and the Lisburn Youth side, Paul worked his way through the youth set-up at the club and was always an intelligent striker. Not blessed in height, he used his running to make space for himself and others and was sharp enough to be in the right place at the right time to score.
His appearance on the Tottenham first team scene was marked with a goal against Coventry City at White Hart Lane in his third game, but McVeigh failed to make the breakthrough into the first team squad as a regular, as there were the likes of Teddy Sheringham, Les Ferdinand, Chris Armstrong and Steffen Iversen in front of him. An ankle ligament injury picked up in pre-season training for the 1997-98 season interrupted his presence in the first team squad and when fit, he had lost his place in the pecking order. Despite playing well in the reserves for a couple more seasons, a change in management brought more new forward signings, so, Paul left White Hart Lane in 2000 to join the Canaries where he had his fair share of success in the side, helping them to the First Division play-off final in 2001-02. While that was not a successful season, McVeigh did play a part in the Norfolk club winning the 2003-04 First Division title.
Having difficulty getting a regular place back in the Norwich team, Paul decided to put his international career on hold in 2004, which has led to him not being re-considered for the Irish side since then.
With his time up at Norwich City, McVeigh had trials with Pisa in Italy and at Plymouth Argyle in the summer of 2007 before he signed on with Luton Town in a season that saw them relegated because of points deduction as they went into administration and start the next season with an even greater handicap because of financial mis-deeds off the field. This meant they had to let some players go and McVeigh was among them, leaving him without a club to start the 2008-09 season. Paul headed for the USA and had a trial with the San Jose Earthquakes, but he returned to England and the striker found a place in the squad at newly relegated Norwich City, but a quick change of manager saw him get little first team action under Paul Lambert and he was released by the club following their promotion back to the Championship.
Since being released by Norwich City, Paul has worked as a motivational speaker.