The Society of London Theatre (Solt), which represents all the West End venues, had proposed giving one performance at every theatre on Sundays and closing Monday nights when audiences are usually sparse.
A 5 per cent across-the-board pay rise was offered to backstage workers but, in a ballot organised by their union, Bectu, 92 per cent voted to turn down the offer.
A narrow margin of 52 per cent agreed in a separate vote to continue discussions with Solt on the issue. But prospects of Sunday opening in the near future are now non-existent.
Solt was particularly anxious that theatres should be open on Sundays by the end of this year to cash in on the large number of visitors expected in London for the millennium celebrations. The Society had proposed a "Millennium Experiment" with all theatres giving Sunday performances from October this year until March 2000.
But Bectu members decided that not only was the pay increase too small, their quality of life would suffer. Jim Johnstone, a national official with the union, said: "West End workers already work a six-day week including Saturday. The proposal as it stands would mean working through the entire weekend and so losing any chance they had of spending time with their partners and children.
"The union has now invited management to reconsider their financial offer and consider ways that members can be guaranteed quality time off."
A survey by Mori found that one-third of theatre-goers said Sunday performances would make them visit more often, with younger people most likely to increase visits. London's theatres have had difficulty in attracting young men in particular. The survey found that among audience members under 25, women outnumber men by seven to three.
Jamie Wells, of E&B Productions, whose recent West End shows included Annie and Kat and the Kings, said: "It's crazy. We're in the entertainment business and we're not entertaining on one of the two weekend days."
Three West End shows - ART at Wyndham's Theatre, Buddy at the Strand and the Reduced Shakespeare Company at the Criterion - have played on Sundays after separate negotiations with their staffs.
"We get a lot of tourist trade, a lot of door trade on Sundays," said Dafydd Rogers, the associate producer of ART. "Our Sunday takings are as high as any other day."
Peter Morris of Solt said: "We will not let go of this. We will continue to try to thrash out a Sunday-working deal and will get round the table with them again.
"At least a majority of Bectu members did vote to continue talking. But it is now obviously too late for the experimental period we were originally proposing."Reuse content