The first group of 15 was intercepted after an alert at 11.30pm on Sunday.
Just after 4am on Monday, another small boat with eight people on board was discovered.
Border Force ship HMC Vigilant and its smaller Hunter patrol vessel picked up both groups, who were taken to Dover.
They have had medical check-ups and will be interviewed by immigration officers.
There is no information on nationalities, but the vast majority of those picked up in the recent spate of crossings have been Iranian.
:: Why are more migrants trying to cross the Channel?
More boats were also discovered off Kent on Sunday morning, with 16 people picked up in separate incidents.
Home Secretary Sajid Javid has designated the rise in crossings a “major incident” but earlier this month expressed doubt about whether migrants are “genuine” asylum seekers.
He questioned why they do not seek help in the first safe country they reach, such as France.
UK and French authorities say they are working together stop the crossings and have had success in arresting suspected people smugglers, who often charge the migrants thousands.
But there are fears some of the small dinghies may have sunk without trace in the Channel – the world’s busiest shipping lane.
Meanwhile, up to 170 migrants are feared dead after two accidents in which dinghies sank in the Mediterranean last week.
One of the vessels capsized off Libya after departing the country on Thursday, prompting the Italian navy to stage a rescue operation.
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