Figures show that allegations of sexual assault on board an ocean liner are being reported at the rate of one a fortnight to investigating authorities.
Travel organisations are concerned about the damage these attacks will do to the cruise industry which is expected to attract more than 800,000 British holidaymakers next year.
They are calling for cruise operators to adopt stricter vetting procedures for their staff, who have been largely blamed for the rising crime figures.
Many of these attacks, which are being investigated by the United States Federal Bureau of Investigation (FBI), have been carried out on passengers, often young girls, aboard cruise ships touring the Caribbean, which is the second most popular destination for British tourists. Some assaults happened on ships regularly used by British holidaymakers.
In one case, an American woman accused a waiter of raping her after drugging the dinner she shared with her husband. In another incident, the victim claimed the ship's bartender raped her 16-year-old daughter after she celebrated her birthday on board, and in a third case it was claimed that a crewman broke down the woman's cabin door to rape her.
The crimewave is also being blamed on falling standards among cruise companies in a mushrooming market. Cruise liners were once the preserve of the very wealthy who paid substantial sums to relax in style on the ocean waves.
Today cruises are accessible to anyone who can afford a decent holiday. Around 800,000 British holidaymakers will go on a cruise next year compared with only 263,400 in 1992 and they could be paying less than pounds 800 for a seven-night cruise, including flights, in the Caribbean.
Many companies advertise cheap mini-cruises lasting only a few days. For example, P&O now runs short-stay cruises from Portsmouth to Bilbao for under pounds 100, and Airtours has just bought a cruise ship.
The Consumers Association says cruise companies have cut their prices to compete with airlines.
"Now you can fly to somewhere nice like Lisbon for an accessible fare which would once have been comparable to a holiday cruise," said a spokesman.
"The cruise companies have had to cut their prices to compete."
Numast, which represents more than 18,000 passenger ship crew members, says many cruise ship operators are employing agencies who hire staff from third world countries because they are cheap, without making checks of their backgrounds.
"There are a lot of operators coming into the cruise market without experience and they have not run to the same standards as the traditional operators," said a spokesman.
"They are taking on staff without checking their qualifications or even whether they have criminal records. What we see now is the tip of the iceberg and the situation has worsened over the past couple of years.
"Ultimately the market will suffer if we continue to see an influx of bargain-basement operators who fly in the face of acceptable standards. We would like the shipping companies to exert stricter controls over who they take on."
Carnival Cruise Lines' Caribbean trips attract thousands of British holidaymakers a year. The company has paid compensation after an allegation of rape against a crew member. It is also facing an action by a US federal grand jury on whether it helped a ship's officer to leave America illegally. Royal Caribbean International is another company which has faced legal action.
There is concern that criminals are taking advantage of the fact that laws of countries such as Britain do not apply at sea, which means they can claim immunity from prosecution. For example, Royal Caribbean claimed that one 16-year-old victim had consented to sex though she had been under age in Florida, which would carry an automatic conviction for statutory rape. The case was settled this summer but the company insisted on a confidentiality clause prohibiting the girl or her lawyer from talking about it.
The FBI has warned tourists to be on their guard on cruise ships where alcohol can make them more relaxed.
"It's an isolated environment on board," said a spokesman. "A lot of people go on these cruises to let their hair down and stumble from one party to the next. Much of what we react to are alcohol-generated complaints although we are not underestimating their seriousness."
The cruise industry is quick to protect itself. Nigel Lingard, chairman of the Passenger Shipping Association, which promotes sea travel, said: "Personal safety on board is the primary concern for all cruise liners who offer cruises to UK holidaymakers. The safe environment a cruise ship offers has helped assist the growth of cruising that the UK holiday market is undergoing."
Carnival Cruises and Royal Caribbean International have defended their safety record and said there were "only a handful" of assaults a year.