A company audit earmarked 2,367 customers and a further 644 unbilled customers called a dedicated amnesty line. Any customers found to be unbilled which don't come forward as part of the amnesty, could receive up to six years' worth of bills in one go.
Thames Water supplies water to more than three million properties across London and the Thames Valley. But many older properties have been divided up over the years and in some cases no-one has informed the company of the change, meaning that separate bills have not been set up.
The audit and the amnesty were launched in parallel on January 20 and identified 1,550 possible unbilled customers in the first week and more than 3000 in the second week.
Mike Tempest, customer services director, said: "We've had 1,509 calls to our amnesty line in the first two weeks of our six-week amnesty, generating 644 leads for us to follow up."
He added: "However, of the 412,299 properties counted by the end of the second week of our customer base audit, 2,367 now are being checked. If we find the occupiers are using water without paying for it, and they don't come forward under our amnesty, they face up to six years of back-charges."