Around a dozen migrants have been intercepted off the Kent coast, following camp clearances in France.
At least two Border Force vessels pulled into Dover on Sunday morning after small boats were stopped in the Channel.
The Home Office said it was “aware of ongoing incidents” as it is believed more UK-bound boats were also caught on Sunday morning.
The coastguard said it was monitoring four incidents off the Kent coast and was working with the Border Force.
A spokesperson said: “We are committed to safeguarding life around the seas and coastal areas of this country.
“HM Coastguard is only concerned with preservation of life, rescuing those in trouble and bringing them safely back to shore, where they will be handed over to the relevant partner emergency services or authorities.”
The number of migrants taken in by the authorities this year is believed to have already passed 1, 000.
On Tuesday, UK Border Force officers intercepted what is thought to be the highest number of migrants in a single day.
Some 86 men, women and children headed to Britain, with some managing to land on beaches before being taken in by officials.
The imminent closure of a gym in Dunkirk, where up to 1, 000 migrants are living, is seen as likely prompting a spike in crossings. Many of those living in the gym are families with young children.
Additionally, on Friday morning French police evicted those living by an area of wasteland and woodland on the outskirts of the port town of Calais.
The same day, the National Crime Agency announced that six people suspected of being part of organized crime groups smuggling migrants across the Channel had been arrested this week.
Last month , Home Secretary Priti Patel said action was needed to put a stop to the crossings.