While recording an episode of Piers Morgan's Life Stories, Miss Brown told the host that the passionate encounter 'just happened'.
She said of Mrs Horner, 46, who married Formula 1 racing team boss Christian Horner in 2015: 'She is going to hate me for this because she is all posh with her country house and her husband, but it's a fact. But it wasn't a thing, it just happened and we just giggled at it and that was it.'
When pressed for more details about their sexual relationship, Miss Brown, 43, said: 'Oh stop it, you pervert', before eventually asserting they did sleep together. In the audience, their bandmate Mel C – whose full name is Melanie Chisholm – said: 'This is all new to me.' Miss Brown, who went through a bitter divorce with her film producer husband last year, added: 'I have said it now. All done. She is going to kill me.'
Although she has not yet publicly refuted the claims, it is thought Mrs Horner is considering making a statement within the next week to 'set the record straight'.
The claim threatens to cause a rift among the bandmates ahead of their reunion tour this summer. Rehearsals for the sell-out shows begin in two weeks, before the first performance in Dublin on May 24.
Miss Brown is known to have a difficult relationship with Mrs Horner – whose departure from the band in 1998 was rumoured to have been due to arguments between the pair. They are said to have already been at loggerheads about outfits for their return to the stage.
The tour is reportedly set to earn the bandmates £2.2million each.
All the former Spice Girls members – including Emma Bunton and Victoria Beckham – remained silent about Miss Brown's claims on social media yesterday. Mrs Beckham is the only one not joining the reunion, which will end at Wembley Stadium in June – 21 years after they performed at the venue as part of their Spice World tour.