Mr Mellor, now a broadcaster and presenter as well as an MP, was unseated from the Cabinet in 1992.
Since then there have been three heritage secretaries in almost as many years, including Stephen Dorrell, now Secretary of State for Health, who was widely perceived as uninterested in the job, and Virginia Bottomley, the incumbent.
In an apparent reference to Mr Dorrell - who, when asked, had not been able to remember the last film he had seen - Mr Mellor warned the National Heritage Select Committee that the post of heritage secretary required genuine interest in the issues.
"You have got to believe that cultural values matter. They're not just a spray-on addition to cultural table talk. Nobody remembers all the emperors Mozart had to slave for, but they remember Mozart," Mr Mellor told the inquiry into the remit and structure of the Department of National Heritage.
"What matters is the motivation and calibre of ministers," he added.
The former minister expressed discontent at the handling of the National Lottery and the Millennium Commission, and gave broad hints that he regretted having to step down from the Cabinet.
"I frankly think there's room for more direction, when you look at what they're planning for the millennium. We're going to get a load of millennium village halls - is that really what we want?"
He also criticised the appointment to the Millennium Commission of Patricia Scotland QC, who is said to have failed to attend meetings.
"In relation to the lottery, it is not self-evident that just because you are a successful female barrister, or have won a gold medal in the bobsleigh, that you are the right person to decide," Mr Mellor continued.
"Parliament should have taken the lead with the millennium. When I see some of the schemes [which have won lottery funding] I wonder which millennium they think they are aiming for."Reuse content