But she refused to talk. She still suffered the memory of childhood abuse by her father and stepmother, Rosemary, but that was not the only reason for her reticence. Phil Walker, editor of the Daily Star, explains: "Our reporters had got to know Anne Marie very well ... There was a sort of meeting of minds. She decided not to talk to anyone else." The Star had also offered her pounds 70,000.
Ms Davis was subsequently called as a prosecution witness in her stepmother's trial, and became one of many people to give evidence against Rosemary West despite their media contracts. These included Janet Leach, Frederick's confessor in custody, offered pounds 100,000 by the Daily Mirror; Caroline Owens, assaulted by the Wests and promised pounds 20,000 by the Sun; and Elizabeth Agius, a Cromwell Street neighbour, paid pounds 750 by ITN and the BBC.
The suggestion that all this money might encourage witnesses to exaggerate formed an important part of Rosemary West's defence. After she was found guilty last week, leading lawyers suggested that if any proof emerged of distorted evidence, the life sentence could be overturned in the Court of Appeal. At the same time, the judiciary resounded with official threats of action. Sir Nicholas Lyell, the Attorney General, said ministers were "seriously considering" making this kind of cheque-book journalism illegal. Lord Mackay, the Lord Chancellor, said that the media's behaviour during the West trial raised "issues of principle" and called for a report. And the Press Complaints Commission, having expressed its concern for weeks, said it would examine the issue at its meeting next Wednesday.
But action against witness buying is problematic. Currently, the Contempt of Court Act of 1981 threatens to prosecute the press if it creates "a substantial risk of serious prejudice of a trial". Yet it is not hard to find lawyers who think this legislation still leaves witnesses open to contamination. "I've sat there and seen some bimbo bargaining with a newspaper," says Mark Stephens, a solicitor who specialises in press cases. "And they say, 'Your story hasn't got much sex in it. Can you do any better?' "
This sort of behaviour, and attempts to halt it, have a rather cyclical history. A witness at the Moors Murders trial in 1966 negotiated a retainer, a holiday, and syndication rights with the News of the World, a deal denounced as "deplorable" by the Press Council, the PCC's predecessor. In 1979 the Sunday Telegraph offered the main witness in the Jeremy Thorpe trial pounds 25,000 for his memoirs - and double if Thorpe was convicted - again to official condemnation. In 1981, even the Queen was moved to express her disapproval at all the witness buy-ups surrounding the Yorkshire Ripper trial, after she received a letter from the mother of one of Peter Sutcliffe's victims.
That controversy led to the PCC's current warning against making payments "to witnesses or potential witnesses in current criminal proceedings". Many would like to see this industry code - often ignored, as codes of self-regulation tend to be - become statutory law: "It just needs to be enforced," says Mark Stephens.
But the PCC's code has loopholes. By covering only "current criminal proceedings", it leaves witnesses open to payments after trials. This could still lead to distortions in their testimony: "You can't prevent people making themselves marketable by being lurid in court," says Clare Connelly, a lecturer in criminal law at Glasgow University who is researching the history of newspaper payments to witnesses.
The code also makes an exception "where the material concerned ought to be published in the public interest and the payment is necessary for this to be done". This is a defence much used by the tabloids: Tom Crone, legal manager for the Sun and the News of the World, invokes the "public interest" within seconds of being asked about payments to witnesses. As Phil Walker, editor of the Star puts it, at the moment "you're talking about the marketplace versus a code that's meant to be simple but is grey as grey can be".
But giving the code more definition, in addition to legal force, is easier said than done. How could offers of money to "lurid" witnesses after a trial be stopped, for example? And a more defined law would still need the official will to operate it; many lawyers criticise Sir Nicholas Lyell, who alone can initiate contempt prosecutions, for failing to confront misbehaving newspapers.
Lord Mackay admitted last week that restricting witness-buying was "not an easy area to operate in". And he continued in the exact terms - including a reluctance to mention cash - that a newspaper editor might use: "People want to read about it [a big trial], and that's what gives rise to the value of these contributions." The West trial judge said payments to witnesses were "a fact of life". The Official Solicitor commissioned a journalist to write Frederick West's biography. Even the BBC and ITN both justify making "small" payments for interviewees' "time" as a competitive necessity, although they deny signing people up to keep their information exclusive.
The public appetite for trial stories gives the justifications for witness buying a certain confidence. Editors insist that they do not sign them up until their evidence has been "crystallised" (they all use the same word) by the police, so any exaggerations can be detected. "We might have been breaching the letter of the PCC code but certainly not the spirit of it," says Mr Walker. Mr Crone goes further: "Very often in these cases the true story is told by the media, not by those in court ... If you say witnesses can never sell their stories, that may stop people coming forward to be witnesses."
In this commercialised environment, where even minor inquiries by the Gloucestershire Echo (which doesn't pay for news stories) are often met by the reply "What's it worth?", curbing payments to witnesses may require a shift in press culture rather than just new regulations. Mr Stephens is still hopeful: "The Roman circus was very popular at the time, but we don't think it's so great now."
And the buyer-takes-all system has its flaws. As in many markets, more choice is the producer's rhetoric and less choice for more money is the consumer's reality. To read about Anne Marie's agonies last week, you had to buy the Star - but then you missed Janet Leach in the Mirror, and Caroline Owens in the Sun. To get every character in the story you had to get every paper.
Scotland could offer an alternative way of doing things. It has no PCC code, but judges are far more ready to prosecute newspapers for contempt and newspapers are far more cautious. Clare Connelly has failed to find any instances of mass witness buy-ups in Scotland to compare with the West trial. "The press appears to be far more responsible ... Until four years ago cheque-book journalism didn't really exist in Scotland," she says. "Until the Sun started operating here."