The Border Force intercepted a small boat crossing the Channel on Saturday while another group of suspected migrants was found in the Kingsdown area of Kent.
In the first incident, the coastal patrol vessel Speedwell and Border Force cutter Seeker were scrambled and 11 men on board a rigid-hulled inflatable boat were detained and brought to Dover, Kent.
A Home Office spokesman said: "All individuals were brought to Dover, where they were medically assessed before being transferred to immigration officials for their cases to be dealt with.
Their nationalities have not yet been confirmed.
"The 11 migrants are now onshore in Dover and will be transferred to Kent Intake Unit for screening."
In the second incident on Saturday, Kent Police and Border Force officials responded to reports of the group of migrants in Kingsdown.
The spokesman said: "A group of 10 people, who have presented themselves as Iranian, have been medically assessed and believed to be well, before being transferred to immigration officials for interview.
"Their nationalities have not yet been confirmed."
He added: "Anyone crossing the Channel in a small boat is taking a huge risk with their life and the lives of their children.
"Since the Home Secretary declared a major incident in December, two cutters have returned to UK waters from overseas operations, we have agreed a joint action plan with France and increased activity out of the Joint Co-ordination and Information Centre in Calais.
"In June, the Home Secretary and the French interior minister, Christophe Castaner, agreed to continue to explore options to reinforce the efforts already being made to cut down on illegal immigrants attempting the crossing.
"It is an established principle that those in need of protection should claim asylum in the first safe country they reach and since January more than 40 people who arrived illegally in the UK in small boats have been returned to Europe."