Lord Tebbit said that the Culture Secretary's "arrogant" handling of the scandal had revived voter anger over MPs' expenses and undermined the Government's message that "we're all in it together", adding: "The best way out of this is for Mrs Miller to resign."
His call came as Labour promised to reform Parliament's standards system in the wake of controversy over the decision of a panel of MPs to overrule a watchdog's judgment on Mrs Miller.
Pressure on the Culture Secretary has been heightened by a poll suggesting that a large majority of voters think she should be dropped from the Cabinet, stripped of her responsibility for press regulation and thrown out of the House of Commons.
The Commons Standards Committee last week overruled Ms Hudson's recommendation that Mrs Miller should repay £45,000 of expenses claimed on a house shared with her parents, and instead told her to hand back £5,800 and say sorry for failing to co-operate fully with the 14-month inquiry. Lord Tebbit said: "Most Members of the Commons must have hoped that the scandals over fiddled expenses had at least calmed down, even if not gone away. Now Mrs Miller has not just re-ignited the flames but, by the arrogance of her response to the scandal, poured petrol on the fire."
Ministers arguing for the need to clamp down on benefit cheats were confronted by "the spectre of Mrs Miller flaunting her twisting and bending of the rules for personal gain on a vastly greater scale and allegedly allowing her staff to threaten unpleasant consequences for those who had caught her out", said Lord Tebbit.
Work and Pensions Secretary Iain Duncan Smith suggested that she was suffering a backlash for being the minister responsible for the same-sex marriage Bill, which was deeply unpopular with many grassroots Tories. Speaking on BBC1's Andrew Marr Show, Mr Duncan Smith said: "I think she has done a very good job in a very difficult set of circumstances."Asked if she should rethink her position, he replied: "No, I don't think so."