Jim Wilkinson was interviewed in 1984 by J. C. Nash for the Society for Industrial and Applied Mathematics (SIAM). The SIAM website describes the interview as:
James H. Wilkinson recalls his early interest and involvement in scientific computing. He recounts his pre- electronic computer calculations at the Cambridge Maths Laboratory and at the National Physical Laboratory in Teddington on applications such as supersonic flow, thermodynamics and ballistics and the importance of getting mathematicians to take numerical analysis seriously. He discusses his postwar work with Alan Turing on the design and programming of the Pilot-ACE and how it informed his work in round off error analysis and solving eigenvalue problems.
The transcript of that interview may be found here.