The 36-year-old former prison officer sold twice as many copies of her single, Skyscraper, than US star Pharrell Williams in second.
Bailey, 36, who was crowned the winner of the singing contest last week, is splitting all proceeds between Great Ormond Street Hospital Children’s Charity and Together For Short Lives, a charity which helps children with life-threatening conditions.
Chancellor George Osborne has agreed to waive VAT on the release.
Robbie Williams held on to top spot in the album chart with Swings Both Ways.
The Take That star’s record was neck-and-neck midweek with One Direction’s Midnight Memories and Gary Barlow’s Since I Saw You Last in a tight race.
But Williams beat off One Direction by fewer than 200 copies after both acts sold more than 126,000.