French patrol boats on Saturday rescued dozens of migrants from makeshift boats in the Channel that were heading to England, maritime officials said.
British interior minister Priti Patel on Friday described the volume of migrants crossing the Channel as "appalling and unacceptably high" and called on France to help keep numbers down.
France's regional maritime monitoring and rescue operation said it acted "on several reports of small boats of migrants in difficulty in the straights" off Calais.
At around 8:00 am a French patrol boat saved 17 migrants aboard two separate vessels northeast of France's port city of Calais, said the operation said in a statement.
About an hour later another boat rescued 16 migrants from another vessel in trouble off Sangatte, which used to host a makeshift camp for migrants heading to England.
Border police serving the Calais region are looking after the 33 migrants, whose nationalities were not immediately disclosed, the statement said.
Since January 1, the French authorities have intercepted at least 810 migrants trying to cross the Channel to England, according to official figures tabulated by AFP.
Later French police reported finding eight migrants in the back of lorry from Spain driven by a Russian national, who they arrested.
The authorities were alerted by the sounds coming from the truck as it was parked at a motorway rest stop near the southeastern French city of Aix-en-Provence. They found five Bangladeshis and three Pakistanis in the back of the lorry.
British interior minister Patel's warning to France on Friday came with London under increasing pressure to tackle the migrant crossings.
During the 2016 referendum in which Britain voted to leave the European Union, Brexit supporters argued for the UK to "take back control" of its borders because of fears too many migrants were arriving.
Last month the interior ministers of France and Britain signed an agreement to create a new joint police intelligence unit to combat migrant traffickers and reduce the number of illegal Channel crossings.
British media reports claim more than 3,400 people have made the crossing so far this year.