The South East Coast Ambulance Service said it was called to an incident at Dover, south England, at around 3:30 am (0330 GMT), where it treated seven people after they were intercepted in the Channel by Border Force officers.
They were all discharged without hospital treatment.
The ambulance crew treated another seven people, again not requiring hospital treatment, in a second incident at around 8:30 am, with the coastguard saying that it was also assisting in the rescues.
All of those rescued claimed to be Iranian, along with the other 64 people rescued in the Channel since November 9.
Nine suspected migrants were rescued in nearby Folkestone on Sunday, while seven were picked up in Dover on Friday.
On one day alone last week, 24 people were intercepted in three separate incidents in Kent.
“We have stepped up deployments of our coastal patrol vessels along the South-East coast in light of recent events,” said the interior ministry.
“Nobody should put their life at risk attempting to smuggle themselves into the UK across the Channel and despite recent events, crossing the Channel in this way thankfully remains relatively rare,” it added.
Local MP Charlie Elphicke said that “not enough is being done”, calling the numbers “unprecedented and deeply concerning.”