John Olsen leaves the company with an unspecified payout at the end of May, to be replaced by Peter Ward, the former head of Rolls-Royce, who left the luxury car maker in February in protest at an engine design deal with BMW of Germany.
Mr Olsen was on a two-year contract with an option to renew for a further 12 months. His pay-off is expected to include a relocation allowance to return from the United States, where he moved in 1993 to take control of the struggling cruise line business.
Nigel Rich, chief executive of Trafalgar House, said Mr Olsen's departure was only partly a consequence of the QE2 fiasco. He had also failed to turn around Cunard, which had suffered from years of under-investment and made a pounds 14m loss in the half-year to March.
It was a bungled attempt to catch up on more successful rivals such as P&O, that led to the public relations nightmare at Christmas when hundreds of passengers were joined on a sailing from Southampton to New York by 2,000 workers struggling to complete a pounds 30m refit of the flagship cruise liner.
Many passengers missed out on the cruise altogether, although most of those who did travel wished they had not. Those who made the transatlantic crossing complained of "Niagaras" of dirty water in the lavatories, corridors blocked by "unsecured materials" and a fenced off swimming pool.
Although Cunard has set aside pounds 7.5m to cover a compensation package, including full refunds, offers of another cruise and spending money, the company still faces a $50m (pounds 31.6m) lawsuit in New York, filed by 120 passengers who claim they were exposed to asbestos during the ill-fated voyage. The action, which could drag on for years if it is not settled out-of-court, calls for individual settlements of $100,000 per passenger. A fund must also be set up against any future health problems and the cost of medical checks.
Passengers are claiming that they suffered "physical injury and emotional distress" because the ship was allowed to sail with several escape routes blocked and some safety doors missing or not working. Since the debacle a number of highly placed staff within Cunard have said it was plain that the ship was not ready for service when she reached Southampton from Germany for her rededication.
The compensation provision was just one of a string of recent disasters for Trafalgar House, the owner of the Ritz Hotel, which yesterday announced a pounds 48m loss.
The company caused a furore at the end of last year when it launched a hostile bid for Northern Electric. It was the first time that one of the formerly privatised utilities had been bid for.
When Northern attempted to fend off Trafalgar's attentions by offering to pay more than pounds 500m back to shareholders, the industry regulator, Professor Stephen Littlechild, decided to take a fresh look at the companies' profits, sending shares plunging on the stock market.
Mr Rich said Cunard was confident of its case in the $50m litigation, but he admitted that the company would have to do more "to avoid the silly things that have happened".
Cunard's new boss has a background in service industry marketing, having worked at the Mandarin hotel group in Hong Kong, which like Trafalgar House is now part of the Jardine Matheson trading empire.
Outlook, page 33