At least two Border Force vessels, carrying what appeared to be around a dozen migrants in orange life-vests, were seen pulling into Dover on Sunday morning.
It is understood more UK-bound boats were caught before reaching British shores - although events are still unfolding.
The Home Office said it was "aware of ongoing incidents".
It comes days after Border Force intercepted what is thought to be the highest number of migrants in a single day amid warnings the closure of a French camp could prompt a spike in Channel crossings.
Some 86 men, women and children attempted the journey in small boats on Tuesday, with some managing to land on beaches before being detained.
Refugee charity Care4Calais warned the imminent closure of a gym in Dunkirk, where up to 1,000 migrants are living, is likely to prompt a spike in crossing attempts.
On Friday morning, French police officers - including some apparently armed with tear gas guns - cordoned off the road by an area of wasteland and woodland on the outskirts of the port town of Calais, telling those camping there to leave and move their tents.
The wave of migrant camp evictions and the looming clearance of a Dunkirk gym - currently thought to be housing more than 70 families, many of whom have young children - came after a French court order was issued.
On Friday, the National Crime Agency said six people suspected of being part of organised crime groups smuggling migrants across the Channel in lorries and small boats had been arrested this week.
The number of migrants taken in by UK authorities so far this year is thought to have already passed 1,000.
Border Force cutters are continuing to patrol the Channel while drones, CCTV and night vision goggles are used.
Last month, Home Secretary Priti Patel said urgent action was needed to put a stop to the tide of crossings, after she met French interior minister Christophe Castaner in Paris.
More detail on the action plan is yet to be released.