Despite being something of a latecomer to the download world, Woolworths' is differentiating itself by offering every track that appears in the top 50 singles chart and the top 100 album chart.
Jim Batchelor, head of entertainment at Woolworths, said: "Our site will make sure that new music and tracks that are popular now enter the official download chart. We aim to give our customers the widest possible choice of music, making digital music more accessible than ever."
The service has the backing of boyband singer Anthony Costa from the band Blue.
"Digital tracks are a new and cool way for fans to play music. A big name like Woolworths coming into the market is good news for music lovers, record companies and bands. We've been on the site today and downloaded tracks by George Michael and Simply Red," Costa said.
At the same time, independent record companies have accused Apple of wasting time in signing artists such as Franz Ferdinand and The Kills, saying that the company has refused to negotiate terms for their artists.
Franz Ferdinand's label Domino Records has not yet seen its artists appear on iTunes, despite having signed a contract with the service.
Harry Martin, head of Domino, told the Financial Times: "I can only think iTunes Europe is under-resourced or struggling."
Apple said that it was working to get music from Domino and other independent labels live as quickly as possible.
Apple's iTunes service in the UK is also facing investigation from the Office of Fair Trading after the Consumers' Association highlighted the fact that tracks costing 99 cents in France and Germany cost the equivalent of €1.20 in the UK.
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