Chief executive Peter Rogers told LGC he had decided to let Mr Cook go after what he described as problems with 'organisational fit'.
Mr Cook took up the finance post at Westminster in March after losing his job as chief executive of Daventry DC last year. His departure from Daventry was at the time blamed by Labour members on the new Conservative administration's 'resentment' over his success (LGC, 4 November 1999).
Sources close to Tory-run Westminster claimed Mr Cook's relations with members had played a key part in his latest exit.
Describing Westminster as a 'particularly demanding' authority, he added: 'You are always disappointed when you make an appointment and it doesn't work out. To some extent when you let anyone go it's a reflection on you and your judgment. But the one thing you can never predict is how someone will fit into an organisation.'
Mr Cook said: 'I'm leaving Westminster for family reasons and to concentrate on my own personal business interests in a different part of the country.'
But, in a pointed statement to LGC, Mr Cook made it clear he found the step down from chief executive to finance director problematic: 'It was far from ideal to be a second in command. I expect to continue working with the more progressive side of local government in a number of new areas, to be announced shortly, but not in direct employment. This will enable me to use my abilities, skills and experience more constructively and professionally.'
In dispensing with Mr Cook's services before the end of his six-month probation period, Westminster has avoided having to pay him a substantial redundancy sum. The finance post was offered with a salary of up to£100,000 a year, plus performance related pay of up to 25%.