Campaigners sought to highlight China's human rights record
Mr Hu Jintao, who is widely expected to be China's next president, is also due to have meetings with the Queen and Bank of England governor Eddie George during his five-day trip.
He had a mixed reception on his arrival in Britain, facing protests by pro-Tibetan campaigners and human rights activists but greeted with cheers by pro-China supporters.
Protesters also maintained a visible presence as Mr Hu talked with Mr Blair at Number 10.
It is the vice-president's first visit to the West and follows his meeting with Russian President Vladimir Putin on Saturday.
The two men discussed the war against terrorism, events in Afghanistan and the prospects for a post-Taleban government there.
Mr Hu and his delegation were led into Downing Street through a side entrance to avoid a crowd of about 40 protesters.
Little known
Mr Hu is hardly known outside his homeland and his trip to Russia, the UK, France, Spain and Germany is being seen as a chance for him to step out onto the world stage.
Members of the Free Tibet Campaign say they will hold peaceful protests during his stay, including Monday's demonstration outside Downing Street.
They are targeting him because of the hard-line he adopted when he was in charge of Tibet in the late 1980s.
Protesters have called for Mr Blair to press his guest to open unconditional negotiations with the Dalai Lama's Tibetan government in exile.
One said: "We do not want Tibet to be a casualty in securing China's unconditional support for the allied bombing in Afghanistan."
Terrorism agenda
The 11 September attacks on the United States have thrust the tour into the international spotlight.
Mr Hu is the first Chinese leader to visit the West since those attacks took place and America's response to them looks set to dominate his discussions.
"The objective of the visits is to strengthen our friendship and cooperation with the various countries," a Chinese foreign ministry spokesman told the French news agency AFP.
"During the meetings with the leaders of the countries he will exchange views on issues of common concern, including the fight against terrorism."
Close scrutiny
Mr Hu, 59, ranks fifth in the Communist Party's seven-member Politburo Standing Committee and is its youngest member.
He was anointed successor to President Jiang Zemin by the late paramount leader, Deng Xiaoping, and will replace him as leader of the party next year.
He will then take Mr Jiang's place as president when the latter steps down in 2003.
Outside the Communist Party inner circle, very little is known about the Chinese vice-president.
But every detail of his visit to the West is likely to be scrutinised minutely, not only by the individual governments, but also by his own colleagues back in Beijing.
As one analyst in Beijing put it, his performance could affect his political fate.