The Ministry of Defence will instead deploy additional military aircraft for surveillance and provide personnel to help the Border Force after the home secretary, Priti Patel, lodged a request for support.
Saturday’s announcement came after the UN Refugee Agency (UNHCR) said the deployment of warships could cause “fatal incidents”.
A joint statement with the International Organisation for Migration (IOM) said the agencies were “troubled by the proposal to intercept boats and return those attempting to cross the English Channel irregularly”.
“The foreseen deployment of large naval vessels to deter such crossings and block small, flimsy dinghies may result in harmful and fatal incidents,” it added.
“Although increasing numbers of people have been crossing the Channel by boat this summer, the numbers remain low and manageable. People forced by wars and persecution to flee their homes and people on the move frequently embark on risky journeys in many parts of the world. Saving lives should be the first priority.”
The UNHCR and IOM called for the British government to increase search-and-rescue efforts, combat human smuggling, expand legal options for seeking asylum, and make family reunion rules less restrictive.
The Independent understands that the navy may consider deploying ships again in future, but officials have questioned how they would contribute to the work currently done by Border Force vessels.
Stormy weather conditions are expected to decrease the number of crossings over the coming days, and talks are continuing with France over how to bolster security along its coastline.
The last military ship sent to the Channel was HMS Mersey in January 2019, after Sajid Javid declared a “major incident” as home secretary.
Several naval vessels were previously deployed in the Mediterranean as part of the EU’s Operation Sophia mission during the refugee crisis that started in 2014.
More than 4,000 migrants have crossed the English Channel in small boats so far this year, including at least 600 in recent days.
The home secretary formally lodged a request for support with the Ministry of Defence last week and A400M and P-8 Poseidon aircraft were sent for surveillance within days.
On Saturday, the defence secretary announced that a Shadow R1 aircraft would be added to track vessels and pass information to the Border Force, alongside a team of Royal Navy planning and logistics personnel.
Ben Wallace said: “These dangerous crossings ultimately put people’s lives in danger and it is right that we support the Border Force by providing specialist capabilities of defence, and our expert personnel to stop this criminal behaviour.”
A Ministry of Defence spokesperson said officials remained in contact with the Home Office and would “provide further assistance if requested”.
The mayor of Calais previously said the deployment of warships in French waters would amount to a “declaration of maritime war” .
Natacha Bouchart appealed to Boris Johnson to “calm down” and change tactics.
But a YouGov poll found that 71 per cent of British adults backed the idea of the Royal Navy patrolling the Channel to stop migrant crossings, and 69 per cent supported the RAF working with the Border Force.
Ministers have been accused of “stoking tension and division” with comments on the crossings, after the prime minister called the journeys “very bad and stupid and dangerous and criminal”.
A former royal marine has been put in the new post of “clandestine Channel threat commander”, but the Home Office denied claiming migrants present a threat.
The government was warned nine months ago that its own policies were “pushing migrants to take more dangerous routes” across the Channel in an official report by MPs.
Ms Patel was a member of the Foreign Affairs Select Committee when it heard evidence that the number of migrants trying to reach the UK by sea would increase and current measures were not working.
The resulting report called for the government to increase legal routes to seek asylum, improve “dire” conditions in French camps, and address the root causes of migration.
Chris Bryant, a Labour member of the committee, told The Independent the current situation “wasn’t only predictable, but we predicted it.”
He said measures previously billed as “clampdowns” had been “notoriously ineffective”.
Last month, the UK and France launched a new intelligence-sharing unit intended to crack down on smugglers, and millions of pounds have been spent in the last 10 years on bilateral arrangements aimed at stopping migrants leaving France.
Mr Johnson has suggested that the government will push for a change in the law to “send away” more people who reach the UK across the Channel.
Downing Street claimed that Brexit would allow the UK to draw up a new framework for dealing with migrants outside the “inflexible and rigid” Dublin regulation.
The UK has already made hundreds of deportation requests under the law, which requires asylum seekers to claim asylum in the first safe country they arrive in.