9:38 was thought up by three church leaders: Richard Coekin, Ian Garrett and Vaughan Roberts, in the mid-1990s. The three were particularly concerned that there were not enough young people going into full-time gospel ministry and decided to start 9:38 to raise the profile of recruitment, and be part of God's raising up of workers for His harvest field.
With the support of the then-Principal of Oak Hill, David Peterson, and the then-Director of the Cornhill Training Course, David Jackman, they went ahead and formed an executive committee, with David going on to serve as Chairman for over ten years.
Over the years the idea of apprenticeship/ministry training schemes has taken off and evangelical churches across the country of all sizes and denominations now run successful schemes. 9:38 conferences have been a great blessing to many, and a significant step along the way to going into full-time gospel ministry.
For more on the vision of 9:38, see Chris Green's article ‘The Other Lord's Prayer'. And for more on the discussion about a calling into ministry read an article from Christopher Ash or listen to Don Carson answer the question.