A group called Occupy Central is demonstrating about a law that means only candidates vetted by China can stand for the region's top position of chief executive.
Former Bishop of Hong Kong Joseph Zen
One of the leaders is former Catholic bishop of Hong Kong, Joseph Zen.
Speaking to Reuters on Sunday, he said: "It's high time that we really showed that we want to be free and not to be slaves...We must unite together."
Police have been quick to clamp down on the protesters, reportedly using batons and tear gas.
Brian Fung, a student in Hong Kong who was at the protests, told Premier: "We don't have any weapons.
"We are unarmed and we did not fight back at all.
"So I will say the violence was one-sided. It was initiated by the police and we did not fight back at all.
"People were being dragged on the floor. I saw people being attacked with pepper spray on their face and hands and legs."
The Chinese government has warned other countries not to support the "illegal rallies".
Several banks have suspended operations in affected areas, which has led to speculation that markets could crash.
Speaking on Premier's News Hour, Clement Tang, pastor of Luton Chinese Christian Church, showed solidarity with the protesters.
He said: "From a Christian point of view, I think there is a case for civil disobedience because the political system that the Chinese is trying to impose is unjust. It's not fair and lots of the public are actually being awakened to this and want to do something about it.
"China has already blocked all the internet information from the news about Hong Kong. Only the state news version is allowed to be published in China and online."
The Foreign Office says it is carefully monitoring the situation in Hong Kong.
UK authorities are also saying the rights of protesters should be protected.
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