The protests came as US President Barack Obama spoke of the "sense of urgency" needed to confront the financial crisis after he met Prime Minister Gordon Brown at Downing Street.
By Wednesday afternoon the prime minister's spokesman said they were hoping to reach a successful conclusion to the summit.
At the height of the demonstrations, the police estimated there were up to 4,000 demonstrators in the City and officers cordoned off a number of streets.
The BBC's Ben Brown said there had been an "increasingly ugly mood" in Threadneedle Street after protesters smashed RBS windows with missiles, including coins and computer keyboards, and entered the building. The branch had been closed already as a precautionary measure.
Mounted police and riot officers used shields to push demonstrators back and officers said they entered the RBS building just after 1400 BST "in support of building security".
The £703,000 pension arrangement of RBS former chief executive, Sir Fred Goodwin, has sparked public anger.
An RBS spokesman said: "The safety of our employees and our customers is of paramount importance to us."
G20 PLANNED PROTESTS
1100 BST: Financial Fools' Day protesters leave Cannon Street, Moorgate, Liverpool Street and London Bridge stations to march to the Bank of England.
1230 BST: Climate Camp converges on European Climate Exchange.
1400 BST: Stop the War Coalition marches from US Embassy to Trafalgar Square.
1700 BST: Protest on Mall outside Buckingham Palace
However, by mid afternoon the BBC's Danny Shaw said police sources believed the mood had changed, with the atmosphere becoming less tense.
Officers were on the look out for people who were "of interest".
Earlier, officers were pelted with empty beer cans, fruit and flour outside the Bank of England as the crowd of demonstrators had attempted to reach a peaceful climate change protest in nearby Bishopsgate.
Hundreds of Climate Camp demonstrators - behind direct action protests at Heathrow Airport and power stations in North Yorkshire and Kent - pitched tents in protest against carbon markets.
The BBC's Mark Georgiou said there was an "almost Glastonbury atmosphere" at the demonstration outside the European Climate Exchange, which featured "music and meditation".
Several hundred anti-war demonstrators have also marched to a rally in Trafalgar Square from the US Embassy in central London.
The BBC's Dominic Casciani said it had a "completely different mood" to the protests in the City, and demonstrators were in peaceful mood.
Earlier, protest groups under the G20 Meltdown banner had marched to the Bank of England in the City urging those who had lost their homes, jobs, savings or pensions to join them in following four "horsemen of the apocalypse" to "lay siege" to financial institutions.
Many City workers have dressed in casual clothes after banks and other institutions were warned they may be targeted.
Protester Daniel Blinkhorn, from Brighton, was among those marching from London Bridge station to the Bank. He said the G20 leaders had a "real opportunity to green the global economy".
Housing association worker Tony Streeter told the BBC: "I'm here because I think people are angry about what's going on in the world there's too much greed."
Scotland Yard said a total of 23 people had been arrested in connection with the protests, including four on Tuesday.
The four people were charged after officers were alerted to a group trying to break into a building in the Holborn area of central London, police said.
On Wednesday, police questioned demonstrators travelling in an armoured vehicle dressed in helmets and overalls.
Police say 11 people have been arrested on suspicion of possessing police uniforms and for road traffic offences.
Six police forces are part of the £7.5m security plan, led by London's Met.
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