HMS Tyne was deployed as part of a NATO operation to shadow Russia 's submarine Krasnodar as it surfaced back to the country from the Mediterranean.
Police say they are trying to establish the identity of a man who died crossing the English Channel.
So far this year 6,796 people have arrived in 123 boats - with increasing numbers of passengers being crammed onto fewer boats.
More migrants have been brought ashore at Dover after crossing the English Channel in small boats.
French authorities said the overcrowded boat set off close to the port of Dunkirk on Wednesday evening.
Two British warships were deployed to escort a pair of Russian military vessels from the English Channel, it has been revealed.
Armed personnel were seen manning machine guns on the Boikiy, a 343ft-long Russian corvette that can carry up to 99 men at a time.
The campaign is underway amid a 20 per cent increase in illegal migrants who made the journey this year, with the total standing at 2,716 so far.