Demonstrations against the monarchy take place in London as well as in Glasgow in Scotland and Cardiff in Wales.
Republic said its leader Graham Smith had been detained on Saturday morning and a photo posted on Twitter showed him sitting on the ground surrounded by police officers.
The group had said it would mount the biggest protest against a British monarch in modern history. Protesters wore yellow t-shirts to stand out and held up signs saying, “Not My King”.
They spent most of the service booing or singing songs, such as “He is just a normal man”.
However, London police had warned they would take action if protesters tried to “obstruct the enjoyment and celebration” of the day, and they formed a ring around the group.
“It is disgusting and massively over the top,” said Kevin John, 57, a salesman from Devon who was among the protesters.
“It is also hugely counterproductive by the police because all it has done is create a massive amount of publicity for us. It is completely crazy.”
Police did not confirm Smith’s arrest but said they had arrested four people on suspicion of causing a public nuisance and three people on suspicion of possessing articles to cause criminal damage in what they called a “significant police operation”.
Republic said hundreds of its placards had been seized.
Protests also took place in Glasgow in Scotland and Cardiff in Wales, with signs held up saying, “Abolish the monarchy, feed the people.” On social media, many contrasted the cost of living crisis in the United Kingdom with the pomp and pageantry on display at the coronation.
‘A true democrat’
Royal biographer Christopher Wilson told Al Jazeera that the king has seen protesters all his life and is used to demonstrations.
“He, I think, is a true democrat who believes in freedom of speech,” he said.
“The republic movement is not in any way a terrorist movement. It’s simply a voice of protest and they have a right to free speech. After all, Britain is supposed to be the cradle of democracy. Free speech is one of the great tenets of our life,” he added.
Although the protesters were in a minority compared with the tens of thousands gathered on London’s streets to support the king, polls suggest support for the monarchy is declining and is weakest among young people.
With the crown passing from Queen Elizabeth to her less popular son, republican activists hope Charles will be the last British monarch to be crowned.
While many other European monarchies have come and gone, or are far diminished in scale and importance, the British royal family has remained remarkably resilient.
In the UK, polls show the majority of the population still wants the royal family, but there is a long-term trend of declining support.
A poll by YouGov last month found 64 percent of people in the UK said they had little or no interest in the coronation. Among those aged 18 to 24, the number voicing little or no interest rose to 75 percent.
More than 11,000 police officers are on patrol for the coronation, the biggest ceremonial event staged in the British capital for 70 years.