Fraud can be treated as a criminal or civil matter for legal purposes.
For it to be criminal fraud, which is an offense against the state, the SFO (fraud prosecuting authority, equivalent of the CPS) has to have enough evidence to bring the individual or company before a magistrates' or crown court, leading to a fine, probation, or imprisonment if the defendant is found guilty.
The SFO must prove intent to deceive and defraud 'beyond reasonable doubt', which is very difficult, and will be more likely to prosecute depending on the seriousness of the crime, whether the victim was vulnerable, whether the fraudster was in a position of responsibility, the likelihood of recovering the assets. It would not even contemplate taking a case against SW for the CB Prize.
Most fraud cases go the civil route, where the burden of proof is lighter ('on the balance of probabilities') and it's a matter between private individuals or companies, rather than the state and an individual, and where the purpose is to compensate the victim of the fraud for their financial losses.
But in order to do either, the RSL would have to take legal action, claiming loss or damage because of reliance on an intentionally false statement made with the intent to deceive. And even if they wanted to start to mount a potentially expensive civil case (they would not have the faintest chance of a criminal one) -- the RSL wasn't subjected to a financial loss by SW winning the CB prize. If she hadn't won it, the £10k prize would (almost certainly) have gone to another writer.
I can't see the trustees of the CB Prize, however annoyed they might be that the first time the prize was awarded, it went to someone ineligible, starting a public fuss about this. It would only drag a newish prize founded in honour of a loved one into disrepute.
I imagine their first concern would be to talk to the RSL about what their due diligence is in checking eligibility. Though, as an agent or publisher puts an author forward, not the author, presumably they're the ones signing something to say that to the best of their knowledge this author is a first-time author. But after that, if Google doesn't bring up anything published under the same name, and the author says they haven't previously published a book, I'm not sure where you would go?