But her plans for chart domination could be ruined by dance act Spiller - whose track Groovejet (If This Ain't Love) has dominated radio and club playlists in recent weeks.
Beckham's first non-Spice Girls track, Out of Your Mind - also featuring vocalist Dane Bowers - hit record shops on Monday, a day after Sporty Spice's I Turn To You was confirmed as the UK number one.
But her plans for chart domination could be ruined by dance act Spiller - whose track Groovejet (If This Ain't Love) has dominated radio and club playlists in recent weeks.
The 1970s-influenced record features the voice of 21-year-old Sophie Ellis-Bextor, who had limited success with London-based band Theaudience in 1998.
The track was featured on TV promotions for BBC Radio 1 earlier this year.
Despite the record's enormous success in clubs, the daughter of former Blue Peter presenter Janet Ellis has said she never listens to dance music, and finds the song's success "pleasant but ludicrous".
Ellis-Bextor has done very few press interviews to promote the Spiller track, while, in contrast, Beckham is following the regular round of media interviews.
She told ITV breakfast station GMTV on Monday morning she was swapping her trademark short hair for longer locks, thanks to permanent hair extensions.
The Sun reports she and Dane Bowers were "left raging" after DJs at an Ibiza nightclub played the Spiller track minutes before the duo were due on stage to perform Out Of Your Mind on Saturday to 5,000 revellers.
She is reported to have said: "This music's a bit too hardcore for me."
Beckham, footballer husband David and Bowers were mobbed by hundreds of screaming fans when they made an appearance at London's Virgin Megastore on Monday.
The trio signed copies of Out of Your Mind and assorted Spice Girls memorabilia.
One fan, 14-year-old Samantha Wilkinson from Tottenham in London, said: "You really expect celebrities not to be so nice, but they were. They're just so normal."
Her friend, Laura Hanna, 15, added: "I am really happy because Posh hugged me."
American superstar Britney Spears is also involved in the fight for the number one spot with her latest single, Lucky.