In a wide-ranging speech, Brown also suggested that the International Monetary Fund (IMF) be turned into an independent watchdog.
He said the IMF could be the key part of a global early warning system monitoring financial risks.
Brown said Britain would play a role in efforts to speed up nuclear disarmament "and to ultimately achieve a world freer from nuclear weapons".
London would also press for early agreement on a new international system to help non-nuclear states acquire new sources of energy, he said.
"I propose that the IMF should act with the same kind of independence as a central bank in a national country"
Gordon Brown, Britain's prime minister
Brown, who visited China before the visit to India also called for the creation of a multi-billion-dollar global climate change fund.
He said the fund could be placed under the remit of the World Bank to finance environmentally sustainable development in poor countries.
Brown said that India played a "very notable" role in talks for a post-Kyoto Protocol agreement on Bali last December.
"From Bali I'm positive about the constructive role that Britain and India can play in bringing about a climate change agreement," he said.
India has in the past appealed to developed nations to give more assistance so it can employ cleaner energy technology.
Referring to the global credit crisis that began last year after problems in the US sub-prime mortgage market, Brown said failings in global financial supervisors should be addressed.
"I propose that the IMF should act with the same kind of independence as a central bank in a national country," he said.
"It should make its focus the surveillance of the global economic and financial system. Its role should be to prevent crises and not simply to manage or resolve them as in the past," Brown said.
"The IMF, working with the global Financial Stability Forum, should be at the heart of ... an early warning system, involving regulators and supervisors in all countries, for financial turbulence affecting the global economy."
The Financial Stability Forum groups central banks, regulators and international bodies.
UN recovery fund
The global 'credit crunch' led to a run on the Northern Rock bank in Britain last November, the first run on a British bank in more than a century.
Northern Rock has borrowed about £26bn ($50.9bn) from the Bank of England.
Brown will meet the leaders of France, Germany and Italy in London on January 29 to discuss a response to the crisis.
While backing India's bid for a permanent place on an expanded UN Security Council, Brown said the world must do more to ensure that reconstruction got under way rapidly after conflicts.
He said that rapid response teams of police and experts could be created to restore order and begin rebuilding immediately after conflicts.
In addition to suggesting rapid response teams, Brown said he would ask Ban Ki-Moon, the UN secretary-general, to launch an appeal to raise money for a new UN crisis prevention and recovery fund.