The mission -- named "Operation Sophia" for a baby born on an EU rescue ship -- was launched in May last year after almost 700 people drowned when their boat capsized
off the coast of the Italian island of Lampedusa.
Following the tragedy, it was hoped Operation Sophia would fight smugglers and stem the tide of people making the dangerous sea voyage from Libya to Europe.
While the mission has rescued about 9,000 migrants at sea, it "does not, however, in any meaningful way deter the flow of migrants, disrupt the smugglers' networks, or impede the business of people-smuggling on the central Mediterranean route," said Britain's House of Lords EU Committee.
Patrolling a vast area of the high seas between Libya and Italy, the EU ships have been tasked with gathering information, rescuing migrants, and destroying boats used by people-smugglers.
But the parliamentary committee found that "the destruction of vessels has simply caused the smugglers to shift from using wooden boats to rubber dinghies -- which are even more unsafe."
The EU naval mission had so far only made low-level arrests of targets, said the committee.
The report added that there were also "significant limits to the intelligence that can be collected about onshore smuggling networks from the high seas."
While Operation Sophia had been a valuable search and rescue mission, it had failed to tackle the root causes of people smuggling, said the committee, adding: "It responds to symptoms, not causes."
An EU spokeswoman said in a lengthy statement to CNN that the mission had made "substantial achievements in a short period of time."
"After only seven months of operation at high seas, Operation Sophia has contributed to apprehend and transfer to relevant Italian authorities 69 suspected smugglers," the statement said.
"The Operation served as a disincentive for traffickers and brought an important contribution to building better knowledge of these criminal networks and making their work more difficult and less profitable. They no longer can operate in impunity in high seas."
The mission now hopes to expand its operation to Libyan territorial waters -- though this depends on first receiving an invitation from the Libyan government.
Migrants fleeing the civil war in Syria continue to head toward Europe, with another 500 people feared dead last month
when their boat sank between Libya and Italy.
It follows the deadliest year on record for such deaths
, with more than 3,700 migrants dying while crossing the Mediterranean to reach Europe in 2015, said the International Organization for Migration.
By comparison, 3,279 migrant deaths were recorded in the Mediterranean in 2014.