A 15ft motor cruiser was reported in trouble off St Margaret's at Cliffe near the Kent coast at 08:00 BST.
Dover lifeboat and a Border Force cutter were launched and the cruiser was towed to safety.
The Home Office said two European Economic Area nationals were on board the vessel.
A spokesman said Border Force officers were checking the validity of their documents.
Two people rescued in the English Channel after sending a distress signal are being questioned by Border Force officials.