Davenport was born in Birkenhead and was spotted by scouts from Nottingham Forest while playing for Cammell Laird in the West Cheshire league.
While a Forest player, Davenport won his only senior cap for England in a 2–1 friendly win over the Republic of Ireland on 26 March 1985.
A hectic fixture schedule followed, with 10 games being played between Davenport's arrival on 12 March leading up to his first goal in a 4–0 win over Leicester City on 26 April.
Davenport scored his seventh goal of the season on 4 November 1986, but it came as United were thrashed 4–1 by Southampton in the fourth round replay of the League Cup.
[6] Davenport signed for nearby Sunderland in the summer of 1990, and formed an effective strike partnership with Marco Gabbiadini in the first half of the season.
Despite the fact that he had played for Manchester United and Nottingham Forest in the 1980s, both teams who fairly regularly won trophies around that time, this was Davenport's first and only appearance in a major cup final.
After his football career finished, Peter Davenport went on to coach rugby and teach at St Anselm's College in Birkenhead.
[7] In June 2001, Davenport was appointed as manager of Bangor City in the Welsh Premiership, where he took the team to three third-place finishes in four years qualifying for European competition 3 times.
Davenport resigned from his post in December 2005 citing a lack of progress in the Welsh premier league and Bangor's unsuccessful application to build a new stadium as his reasons.
[12] His sacking an acrimonious one, blaming the chief executive, Haydn Preece, personally for his demise quoting that he felt he was "stabbed in the back".