Four boats carrying 72 migrants were intercepted by Border Force off the coast of Kent and Sussex on Sunday.
The first two boats were intercepted at 06:30 BST and were carrying 22 men and eight women, who identified as Iraqi, Iranian and Syrian nationals.
The third boat was intercepted three hours later with 13 men, who said they were Iraqi or Iranian.
The fourth vessel was carrying 25 men and four women, who identified as Iranian or Iraqi.
All individuals were being taken to Dover to be assessed for any medical requirements before their cases are considered.
Tony Eastaugh, the Home Office's director for crime and enforcement, said those facilitating illegal crossings were "breaking the law" and the UK would seek to return anyone with no right to be in the country.
The Home Office said those attempting to enter the UK on small boats were "generally from France" and that French police had stopped more than 90 migrants from "risking their lives" in the past two weeks.
"We are working around the clock each day with the NCA (National Crime Agency) and French law enforcement agencies to arrest and dismantle organised crime gangs in France," Mr Eastaugh said.
Extra police patrols were being deployed on French beaches "on a daily basis", he said, as well as specialist vehicles, drones and detection equipment.
The Home Office said Border Force and all operational staff had personal protective equipment (PPE) available to them.