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.
Advertisement
"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.
More from Calais
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.
