She received much criticism last year for changing the timing of the Fringe so that it began a week before the opening of the official festival. Some venues suffered poor ticket sales and there was confusion among the public.
Yesterday, Ms Strong said the controversy had nothing to do with her surprise resignation. She told The Independent she felt such a key position ought to be held by a Scot. She said: "The move towards a Scottish parliament makes you question these things. The truth is I'm English and it's time to go back where one belongs."
Her remarks will cause a little discomfort for the director of the Edinburgh International Festival, Brian McMaster, who is also not Scottish.
Ms Strong will direct a community production of the Grapes of Wrath in Edinburgh before returning to London to co-write a play. She will then seek another job in arts administration.
In her five years as director of the Fringe she proved a high-profile and largely successful operator, until last year.
Some shows staged in the first week, including a Steve Harley concert, were poorly attended, but the fourth week performances such as Mark Little's stand-up show also suffered when audiences drifted away, believing the festival, which attracts about half a million people a year, was over. Performances including David Mamet's Lakeboat, which should have been one of last year's festival hits, played to disappointing audiences. In spite of the confusion, ticket sales were up 5 per cent. But there were 11 per cent more performances on 1997.
The change of timing, which Ms Strong had explained was due to poor weather in September among other reasons, will continue this year.
Baroness Smith, widow of the former Labour leader John Smith, and head of the Fringe committee said: "Hilary is a great enthusiast with innovative ideas and the personality to put them into practice. We will all miss her greatly."
William Burdett-Coutts, the artistic director of the Assembly Rooms, and an opponent of the dates change, said he was "deeply surprised" by Ms Strong's decision. He added: "I think she has been a very good director and although the compromise between the Fringe and the main Festival is an unhappy one, it would seem to me to be an odd time to be dropping out."
Mr McMaster said: "I've really enjoyed working with her and I'm very sorry to see her go."
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