Rebecca Coriam, 24, from Chester, fell overboard from the Disney Wonder near Mexico. Her body has not been found.
Bahamas police investigated because the ship is registered in the island state, leaving it outside UK jurisdiction.
There are calls for all suspected crimes at sea involving UK citizens to be investigated by the UK authorities.
Former Deputy Prime Minister Lord Prescott said that should be the case whatever the ship's "flag of convenience" - where it is registered.
Ms Coriam's MP Chris Matheson said he feared she was murdered and has called for a UK inquiry.
The Cruise Lines International Association (CLIA) said disappearances overboard were "incredibly rare".
Ms Coriam was last seen alive on 21 March 2011 on board the ship where she worked as a child minder.
Her credit card, which was not found among her personal effects, was used after she vanished.
Mr Matheson said: "I believe there's sufficient evidence to indicate a crime may well have taken place.
"Whatever the circumstance, there's an obligation to investigate. My worst fear is Rebecca Coriam was murdered."
He said it was a "real possibility" she had been killed and the case had not been properly investigated.
"Now is the time for that investigation to take place," he said.
Information collated in the police report from the Bahamas has been shared with the UK authorities, but not with Ms Coriam's family.
Her father Mike said he was "totally baffled and it's upsetting as well" that the authorities in the UK can have a file with instructions not to disclose to the family.
"We're the victims here as well," he said.
Cheshire Police insist the report is not its property to share.
But Mr Coriam said: "It's our daughter. There's been an investigation. Why hold it from us? "
In addition to the frustration over the report, the family has been unable to hold an inquest or a funeral as Ms Coriam's remains have not been recovered.
Under the Flags of Convenience system, ships are registered in offshore nations, often for tax purposes, and if crimes are committed on board it is up to the flag nation to investigate.
National jurisdiction only extends up to 24 miles beyond a coastline - beyond that, the law of the country whose flag the ship flies applies.
The Bahamas sent over police Supt Paul Rolle to investigate Rebecca's case.
Lord Prescott called for an end to the flags arrangement and for a US-style system in which the FBI investigates maritime crimes involving US citizens, no matter where a ship is registered.
Lord Prescott, a former ship steward, echoed calls for an inquiry, saying: "People don't know whether she died or she was thrown over the side.
"What is so alarming is many people are going missing and nothing is being done about it, except for America."
He said there was "almost like a conspiracy of silence" surrounding the case, adding there should be a change in the law as we "should be looking after our citizens".
Bill Anderson, a maritime investigator, said Supt Rolle "only interviewed six people out of just over 2,000-odd people and closed the investigation".
Mr Anderson is "fully convinced" something criminal happened to Rebecca.
The CLIA, the trade body for the cruise industry, said it was the "safest mode of transport".
Disney declined to comment on the case.
You can see more about this story on Inside Out North West on BBC One on Monday 2 November at 19:30 and later on iPlayer.
The mysterious disappearance of a British woman on a cruise ship four years ago should be investigated by UK authorities, campaigners have said.