PARIS (Reuters) -Five migrants trying to cross the Channel to Britain died in French waters in the early hours of Sunday, French local authorities said.

       The small boat overturned as it attempted to launch from a beach in Wimereux, south of Calais, an official told Reuters, adding that one person in critical condition had been taken to hospital in Boulogne, northern France.

       Dozens were pulled from the cold water but the overnight rescue effort was complicated as the waters were too shallow for the French navy's boats that came to help, the local prefecture said in a statement.

       Sea temperature was around 9 degrees Celsius (48 degrees Fahrenheit), it said.

       Those dead are believed to be Iraqi and Syrian, local newspaper La Voix du Nord said.

       British foreign minister David Cameron said reports of the deaths were heartbreaking and showed why Britain had to overhaul its migration system, a key pledge by Prime Minister Rishi Sunak's before an election expected this year.

       Sunak is trying to make headway on his contested plan to deport asylum seekers to Rwanda and legislation to block further court challenges will return to parliament this week.

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       "Ultimately, the only way you can stop the boats is by busting the model of the people smugglers," Cameron told BBC television. "Once we've done that we'll be able to collapse this trade even more."

       (Reporting by Gilles Guillaume and Michel Rose in Paris, William Schomberg in London; Editing by Hugh Lawson)