Mr Nunn, 56, who became artistic director of the Royal Shakespeare Company at the age of 28, and later directed both Cats and Les Miserables, said the state of theatre was such that he could no longer claim it deserved a larger subsidy.
Even more provocatively, he questioned who would wish to visit the West End when it was so filthy - and suggested that the homeless who were clogging up its doorways should be put to cleaning the streets.
"The central area, particularly Shaftesbury Avenue and surrounding Soho, looks perpetually as if a garbage strike is in its second month; gutters are clogged with litter, refuse is scattered everywhere, pavements are sticky with beer dregs, urine and vomit.
"Who of sound mind would pay money to visit such a repellent district in search of entertainment? Every doorway now houses a shivering blanket- huddled person," he wrote in the London Evening Standard.
"There is an obvious equation. Here on hand is a workforce to clean up central London, providing an unrecognisably improved environment for both indigenous and the visiting population, and self-respect and wages for the erstwhile beggar."
In the Seventies and Eighties, he argued, theatrical wisdom was that if you could "hang on" until the tourist season began in June you could then sit back and listen to the turnstiles clicking until late September.
But that was no longer the case. "In the past week, still more West End shows have closed, leaving 10 London theatres empty....
"For the 18 years I was responsible for the RSC, I made regular speeches not only about why we deserved the subsidy we received from the taxpayer, but why it made excellent economic sense to give us more. One of my main points was that tourism, especially of the cultural kind, was the biggest growth industry of the last quarter-century.
"Market research had proved that the British - and especially the London - theatre was a primary reason for people to come to these shores. More Government investment in theatre would achieve a manifold repayment. If I were to make that speech today, I couldn't complain if some men in white coats came to take me away."
Mr Nunn, who joins the National Theatre in September next year, said the solution was for "pusillanimous" managements to stop presenting camp entertainments and unnecessary revivals of "boulevard bonbons in a vain attempt to re-attract yesterday's audience".
In their place, he said, they should stage challenging new plays and new productions of great old plays. It is not clear whether the outspoken views of the millionaire director will offend the National Theatre. A spokeswoman said: "We really don't have a comment."
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