[6] His father, Phil Crump, is an Australian from the country town of Mildura and was riding for the Newport Wasps when Jason was born in Bristol, England.

[7] Phil, a four time Australian Solo Champion (1975, 1979, 1984 and 1988) and 13 time Victorian State Champion, finished third in the world championship in 1976 at the Silesian Stadium in Katowice (Poland) when British star Peter Collins won the title, and as part of the Australian team had won the 1976 Speedway World Team Cup Final at the White City Stadium in London.

Crump didn't place in the 1993 Australian U/21 Championship at his then home track, Olympic Park, and like a number of young Aussie riders was denied the chance to win the title when it was not contested in 1994 or 1995.

Just two weeks following his 19th birthday, Crump rode in his first World Final (1994) held at the Speedway Center in Vojens, Denmark, where he finished in 11th place with six points scored.

Crump won the 'treble' riding for the Peterborough Panthers in Britain during the 1999 season, winning the Elite League, the Knockout Cup and the Craven Shield.

He rode for the Belle Vue Aces for five seasons until the end of 2006 when, in 2007, Crump signed for the Poole Pirates in the Elite League.

At the end of the 2007 season, Poole announced that Crump would be leaving the club due to the large points limit reduction made by the British Speedway Promoters' Association (BSPA) at their 2007 annual general meeting,[12] Crump returned to Belle Vue for 2008 and signed a two-year deal to stay with the club.

[13] However, in October 2008, Crump announced he will not be riding in the British Elite League in 2009 in order to reduce his fixture schedule, allowing him to concentrate on the Grand Prix series.

On 14 September 2009, Crump fell during a last heat decider for Belle Vue against Ipswich, sustaining injuries to his left arm and shoulder.