Viva! 963 was Britain's first radio station for women, launched last July by PR guru Lynne Franks, Debbie Owen, literary agent and wife of Lord Owen, and Labour Party fundraiser Barbara Follett.
It plunged into trouble after it failed to pull in its target 400,000 listeners and has struggled with money and reception problems - across half its London area - which made it effectively unviable.
In January it was forced to make cutbacks and has been operating since then on a skeleton staff from its offices near Marble Arch, west London.
Its latest blow came in March, when RAJAR's official listening figures showed it was the least popular in London, with less than a third of the following of stations like Spectrum, aimed at ethnic minorities.
In all it was pulling only 59,000 listeners for around 20 minutes a day, research which may have finally persuaded its owners, Golden Rose Communications, to sell. However, Golden Rose, which also owns another troubled station, Jazz FM, must now gain shareholder approval for the deal.
Richard Wheatly, chief executive of Golden Rose, said: "We welcome Liberty's involvement in the London radio market with their acquisition of Viva! The resources which Liberty will be able to apply to Viva! I feel confident will, following an anticipated relaunch, result in success."
Stewart Steven, former editor of London's Evening Standard, now the chairman of Liberty, described the purchase of Viva! as "a small but significant building block in the company's plan to create a new and independent media company in Britain".
Under the terms of its licence, Liberty is obliged to continue to aim the station at women aged 24 to 44, and it says that Viva! will stay on air while relaunch plans are finalised.
It will not be an easy task to turn Viva! around after an almost blanket thumbs-down to the new concept of radio for women. Even its own initial research showed that women were surprisingly unliberated when it came to radio listening: if their male partner did not like it they would turn it off.
Their research also showed that women would not listen to a station which smacked of feminism or was "anti- men".
The bid by Mr Fayed, the owner of Harrods, follows his recent acquisition of the defunct Punch magazine for pounds 500,000.
He adds Viva! to his media company, Liberty Publishing, after having been foiled in his attempts to acquire London News Radio, Today newspaper - which Rupert Murdoch chose instead to close - the Daily Express and the Observer, for which he offered the Guardian Media Group pounds 20m.
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