The finding further illustrates the scale of the heroin problem gripping Britain, and Sir David calls on the Prison Service to address the issue urgently by providing increased funding and specialist staff.
He said heroin users experiencing withdrawal symptoms after being admitted to the jail - also known as Walton - were offered a pack of four sleeping pills. "We were informed that, frequently, prisoners took all four pills on the first night, or either sold them on, or were intimidated into handing them over to other prisoners."
The Chief Inspector praised staff working in difficult circumstances with drug users, but said the prison needed a further review of its drug strategy.
"Given the scale of the problems facing the prison, both in preventing drug use within the establishment and with providing effective treatment and rehabilitation services to such a large number of prisoners, the level of existing resources were woefully inadequate," he said.
Drug tests were performed on inmates, but because staff did not carry them out at weekends, "prisoners were able to plan their drug use to avoid giving positive results".
Sir David was shocked to find that, despite the large numbers of heroin users in the jail, staff were so wary of budget pressures that they did not encourage inmates to be vaccinated against hepatitis B, which can be spread by the shared use of needles. He said: "This contradicts government recommendations and the prison's own drug strategy should be corrected immediately."
The report was also critical of the facilities provided for receiving prison visitors, and Sir David called for the jail's anti-bullying strategy to be "thoroughly overhauled".
Martin Narey, the Prison Service director-general, pointed out that the jail had the biggest population in England and Wales. He said a complete review of the anti-bullying strategy was under way, and proposals for a new visitors' centre had been drawn up.