Kydd had been at the forefront of the company's rebranding from NTL:Telewest since he joined in 2006, and was part of the team that signed up actress Uma Thurman to front the £20m relaunch as Virgin Media.
Last year, with Virgin Media facing an unprecedented marketing assault from rival BSkyB, Kydd was credited with helping the brand retain standout in a crowded marketplace.
Under his stewardship, Virgin Media clinched the sponsorship of Channel 4's Big Brother in the wake of the racism scandal that marred the series in 2007, replacing Carphone Warehouse.
Virgin Media lost 19,500 customers in the second quarter of 2008, which was 51,400 fewer than in the same period last year.
Virgin Media said it hoped to appoint a successor by the end of September.
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