A further four boats carrying 65 migrants have been picked up in the English Channel, the Home Office said.
Border Force patrols found the boats travelling towards the UK on Sunday, a day after at least 151 migrants on 15 boats arrived on the Kent coast.
On Saturday the Home Office said it had asked defence chiefs for help.
Immigration minister Chris Philp said he would be in Paris next week to demand stronger measures from French authorities.
He said he wanted to make the route “completely unviable” so migrants “will have no incentive to come to northern France or attempt the crossing in the first place”.