Crews were called out just before 11.40am.
The coastguard was also sent out, as well as Dungerness RNLI after a dinghy containing around 50 people was spotted in the sea, according to reports in the national press.
A spokesman for the Maritime and Coastguard Agency said: “HM Coastguard sent Hastings and Dungeness RNLI lifeboats to assist Border Force with an incident in the Channel.
“HM Coastguard is committed to safeguarding life around the seas and coastal areas of this country as set out in international maritime law and the obligations of the Safety of Life at Sea Convention (SOLAS).
“We are 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.”
Dan O’Mahoney, Clandestine Channel Threat Commander, said: “There is an unacceptable rise in dangerous small boat crossings across the channel because of a surge in illegal migration across Europe.
“People should claim asylum in the first safe country they reach and not risk their lives making these dangerous crossing. We are continuing to pursue the criminals behind these illegal crossings.
“Police patrols on French beaches and enhanced intelligence sharing between our security and law enforcement agencies has helped to prevent crossings through a combination of inland and sea patrols.
“The Government continues to undertake substantial steps to tackle the unacceptable problem of illegal migration through the Nationality & Borders Bill which will protect lives and break this cycle of illegal crossings. The Government is also continuing to return those with no legal right to remain in the UK.”
The Home Office said UK authorities dealt with 14 events involving 430 people yesterday.