Record levels of migrants entering UK
The department said it was taking "substantial steps to tackle the unacceptable problem of illegal migration".
Around 50 people were seen landing on the beach at Dungeness in Kent after crossing in one dinghy.
The group included women and young children.
It comes after eight boats carrying 241 migrants reached the UK on Sunday.
On Tuesday, there were further beach landings at Dungeness and Dover, further along the coast.