Home Office staff have been seen fitting face masks to suspected migrants at Dover.
Pictures showed Immigration Enforcement officers, themselves wearing masks and gloves, processing them at the port.
A total of 25 men and four women in three vessels arrived off the Kent coast between 04:30 and 12:00 BST.
The Home Office said it was "standard practice" for migrants who arrive on small boats to be given face masks, fitted by individuals themselves.
April has been the busiest month on record for small boat crossings, with more than 350 people reaching England.
The Home Office said the coronavirus pandemic was having "no impact on our operational response" to crossings.
In the first incident, at about 04:30 BST, a Border Force vessel intercepted a rigid-hulled inflatable boat (RHIB) which was carrying a group of 12 men and four women, who presented themselves as Iranian, the Home Office said.
Ten men were found in another RHIB at about 04:55 BST. They claimed to be from Iran, Iraq and Kuwait.
In the third incident, at about midday, Border Force was notified of three men coming ashore in St Margarets-at-Cliff. Kent Police detained three migrants who said they were Iranian.
All the suspected migrants were transferred to immigration officials for processing.
More than 800 people have crossed the Channel in small boats this year, including 29 in a single vessel on Easter Sunday.
French authorities rescued 44 migrants - including eight children - from three boats that got into difficulty in the early hours of Friday.
Governments on both sides of the Channel last year pledged to make crossings an "infrequent phenomenon" by the Spring.
Volunteers say migrants living in makeshift camps in northern France are dangerously exposed to coronavirus.
Clare Moseley, of Care4Calais, said she was "very worried" about the potential for the virus to spread, with migrants living in "overcrowded" conditions, without access to clean water to wash their hands.
"That's the worst case scenario," she said.
She added conditions in the camps were "the worst I've ever seen" as many charities have "pulled out" as a result of the pandemic.
Remaining volunteers, who routinely wear face masks and gloves, are focused on meeting a shortage of food and water, meaning toiletries and clean clothes are not being delivered, she said.
As a result, she said personal hygiene in the camps had deteriorated.
"We are seeing people who haven't changed clothes in weeks," she said.
Nine people have so far been taken away by local authorities and placed in isolation after displaying symptoms of Covid-19, Ms Moseley added.