Zuma went to Brown’s Downing Street office for breakfast talks, with Zimbabwe expected to top the menu.
After the pomp of Wednesday’s welcome and state banquet with Queen Elizabeth II, the visit was to focus on trade and diplomatic relations between the two Commonwealth countries.
Zuma and his latest wife, Thobeka Madiba Zuma, were greeted on the steps of 10 Downing Street by Brown and his wife Sarah. Brown shared a joke with the president’s wife as they posed for photographs.
Britain has been a fierce critic of Zimbabwean President Robert Mugabe and his innner circle.
However, Zuma has repeated his call for international sanctions on Mugabe and his coterie to be lifted, saying they were not helping the beleaguered administration.
“If they could lift sanctions, that would give Zimbabwe an opportunity to move forward,” the president said, quoted by The Daily Telegraph newspaper.
Other topics expected to shape discussions are trade, climate change and a global non-proliferation conference in the United States.
Later Thursday, Zuma was to address members of parliament and invited guests at the Palace of Westminster.
And in a bid to boost sporting ties between the two countries, he was also to visit the site of the London 2012 Olympic Games and Wembley Stadium, the home of English football.
The venue, where England beat Egypt 3-1 on Tuesday night, will see Zuma kick a symbolic penalty on the pitch.
South Africa is less than 100 days away from hosting the football World Cup and Zuma will see presentations on England’s bid to host the 2018 tournament.
The president and his wife were also to visit Lewisham Town Hall in south London for talks on youth issues, and a supermarket in Greenwich billed as the world’s first “green” supermarket.
The day was to finish with a banquet at the Guildhall in the City of London, the financial heart of the British capital, thrown by the Lord Mayor and Corporation of London.
Besides the glittering welcomes and political talks, controversy has clouded Zuma’s visit after sections of the British press criticised Zuma over his polygamy and a lovechild scandal.
The president hit back, accusing the papers of colonial attitudes.
Zuma started his three-day trip on Wednesday in a burst of colour and pageantry. He was greeted by Queen Elizabeth on London’s Horse Guards parade ground before heading to Buckingham Palace in a horse-drawn carriage.
At the state banquet, attended by senior royals and political leaders, the queen paid tribute to South Africa’s “extraordinary process of liberation and democratic renewal”.
“The task was daunting in its scale and ambition but was achieved through a deliberate and courageous effort of reconciliation and peaceful resolution of differences,” she said.
Zuma acknowledged lingering problems in his country, saying: “We still have a lot of work to do to create the type of society where all South Africans live in prosperity, with access to basic quality services such as health, education, housing, decent jobs and a host of others.” New African