Sri Lanka went 3-0 up with two dead rubbers left to play later in the week.
Murray played against Poland in September and won both his singles rubbers.
Without relegation in the Premiership a lot of games from January onwards would have nothing at stake and would effectively be dead rubbers.
Turkey's best player, Marcel Ilhan, is currently the world number 119 and would therefore be the favourite to win both of his singles rubbers.
After Italy claimed both singles rubbers on Saturday, world No.15 Flavia Pennetta won her second match on Sunday to ensure her nation will contest November's climax to the tournament.
Switzerland set up Saturday's triumph with two straight sets victories in Friday's opening singles rubbers including a 6-0 6-0 6-2 win for Federer over British world number 262 Alan Mackin.
The host nation needed to win all three rubbers in straight sets to snatch a final spot off the unbeaten Spanish pairing of Maria Jose Martinez Sanchez and Tommy Robredo.
Novak Djokovic's Serbia will play either the U.S. or Brazil after beating Belgium 3-2, having lost Sunday's two dead rubbers as the world No. 1 and Viktor Troicki were rested.
Bresnan said the England dressing room was "a fairly jubilant" place as the team celebrated with bottles of beer ahead of the first of the two dead rubbers next Wednesday.
Jose Maria Olazabal's team trailed Davis Love III's U.S. 10-6 heading into the final day's play, but won eight and tied one of the singles rubbers to retain to the cup.
Smith could give reserve Alex Ward a chance in Sunday's two dead rubbers, which are reduced to best of three sets, but hinted he was likely to stick with James Ward and Baker.
With Britain now trailing Switzerland 3-0, the two reverse singles rubbers left to play on Sunday have been rendered meaningless, though the matches will go ahead although likely to be reduced to best of three sets.
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