"There is a real roadmap for democracy in Egypt," Sisi told BBC television ahead of his visit.
"The Egyptian people have been calling for change for four years. It is our utmost wish to meet their demands and work towards a better democratic future."
After longtime president Hosni Mubarak was ousted in a popular uprising in 2011, Islamist president Mohamed Morsi was voted in.
But Morsi was himself deposed in 2013 by then army chief Sisi, following mass street protests.
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"In the past five years, we have been living in a state of revolution. We want stability. We don't want to do this by force or suppression," Sisi said.
"But Egypt faces monumental problems.
"We are plagued by terrorism.
"No one is oppressed in Egypt. But we're living through incredible times."
Asked about human rights, he said: "What about the millions of Egyptians who face hardship every day? What about their human rights? What about the millions of young people who want a job and education?"
Chris Nineham from the Stop the War Coalition told the crowd: "We are here tonight to stand up against the visit of the dictator al-Sisi, the man who crushed Egyptian democracy".
Another protest is planned for Thursday.
Cameron and Sisi spoke by telephone on Tuesday, and officials confirmed the Egyptian president had arrived in London Wednesday, with talks to begin on Thursday focussing on "security cooperation between both countries," a spokeswoman said.