Fraudsters are likely to buy a pay-as-you-go SIM for a quid, put the minimum top-up value on it, use it for just one transaction (ensuring that they're nowhere near their home when they use their phone) and then simply throw it away. That renders them virtually untraceable.
The police can use the provisions of the Regulation of Investigatory Powers Act 2000 to force phone companies to release data about mobile phone use but they'd probably be unlikely to do so in the circumstances you refer to. (They'd normally only be used for things like counter-terrorism operations or major drug smuggling investigations).