In late 1980, Baker was contacted by Nichola Martin, a producer, music publisher and singer who was setting up a new group to record "
Making Your Mind Up" which was one of the eight songs shortlisted for
A Song For Europe, the winner of which would become the UK entry for the
1981 Eurovision Song Contest. The shortlisting was done on the basis of a recording submitted on
cassette tapes, which was performed by Martin, songwriter
Andy Hill, and
Mike Nolan, but Martin decided to put together a group with two men and two women, not including herself or Hill. The group, called
Bucks Fizz and consisting of Nolan, Baker,
Bobby Gee and
Jay Aston, won
A Song For Europe, which meant they became the UK representative at the Eurovision Song Contest on 4 April 1981. The song went on to win by a margin of four points ahead of the second-placed German entry. O'Connor wrote that "the group sang way off-key, but had such enthusiasm that the judges overlooked this in favour of the song". As part of the choreography, the male members of the group tore skirts off the women at the last chorus, revealing shorter skirts below. Author
Nick Brownlee reflected that "It may sound unkind to suggest that it was this gimmick, rather than the song itself, that captured the imagination of the voters, but such was the relentless sameness of Eurovision songs that it would take something unusual to stir the dozing denizens of Brussels, Frankfurt, Luxembourg and Basle." In Nul Points (2007), his book about Eurovision,
Tim Moore wrote that Baker's "detachable skirt [would] help Bucks Fizz to the Euro crown". Baker later recalled that as the group was on stage being photographed after winning, she thought "That piece of Velcro on the skirts has just changed my life." They had further successful singles, but after
When We Were Young (1983), their next records sold less well. According to journalist and author
Simon Garfield, "petty jealousies over who sang lead vocals and designed outfits and routines" frequently occurred, and Baker would often clash with both Gee and Martin. He refers to the group as "not, after all, a band formed on trust and personal admiration half as much as it was a band formed by the goals of money and success" and therefore prone to infighting and jealousies. In all, Bucks Fizz had 20 singles reach the UK top 60 between 1981 and 1988. The group's popularity had been diminishing before the crash. The group then went through a series of personnel changes after an initial breakup in 1985, with ownership of the name Bucks Fizz being contested. Baker left the group in 1993 to focus on developing her career in television. In an interview with
Boyz in 2015, Baker said that, "When I left the group in the 90s, we were doing bingo halls and places like that and it was soul destroying because no one cared." Baker recalled interviewing participants in a
Here and Now Tour when she was working for a magazine, and being inspired to reform the group. Around Christmas 2004, some of the band members, including Baker, reunited for live performances. ==Television==