Tearfund is looking to Australia to take action on tax evasion as the next country to chair the G20.
The call coincides with the launch this week of the development agency's new campaign, Secret's Out.
Tearfund warns that developing countries have been deprived of up to £555bn because of illicit money flows like corruption, smuggling, laundering and tax evasion.
"It's a shocking statistic," says Ben Niblett, Tearfund's Head of Campaigns.
"And more staggering when you consider the difference that sum could make, helping so many people trapped in poverty. It's why we campaign and keep up pressure to make real changes."
Tearfund is looking to new Australian Prime Minister Tony Abbott to use his position as chair of the G20 to press other countries towards greater financial openness.
"It's not about passing the buck on tackling corruption, it's passing the baton," said Mr Niblett. "Australia is in a strong position to influence other nations, especially South Africa and Brazil, still to adopt similar laws for mining, oil and gas companies.
"Working through local churches around the world, we see the crippling effects of corruption on the world's poorest people. It's often the secrecy around contracts that blights the development of a community. With greater transparency companies become part of the progress with revenue from their operations making a difference to ordinary people's lives."
G20 leaders have already agreed this year to reforms that include the automatic exchange of information on taxes by the end of 2015.
At the G8 meeting in Northern Ireland in June, leaders agreed to "tackle the misuse of companies and legal arrangements" to help clamp down on tax havens.
The European Union has brought in new laws requiring oil, gas and mining companies to publish their payments to governments and earnings in each country they operate in. Similar regulations in the US now require oil, gas and mining companies to publish details of their revenue payments to governments so that citizens can "follow the money".
Tearfund noted, however, that a third of the world is still not covered by transparency laws for extractive industries, meaning some companies are still able to operate outside of the laws and exploit natural resources.
It argues that greater transparency and access to information puts people in a stronger position to hold their governments to account and ensure money is being spent where it is should be.
Tearfund's Secret's Out campaign joins with a global network of churches and individuals in lobbying the G20 and the UK Government to maintain the pressure.
"We are thankful for the US and EU laws, for Canada committing to follow through and the mood for transparent change at the G8 in June," Mr Niblett continued.
"We want Australia's new Prime Minister to prioritise this in the year ahead because we mustn't lose the momentum now when these changes will ultimately help to end poverty."
Bishop Stephen Munga, of the Evangelical Lutheran Church of Tanzania, said: "It's hard to tell where Africa's wealth goes when there's a lack of accountability and public scrutiny – and corruption is shrouded in secrecy. That's why the best way of tackling it is to maximise transparency."
Tearfund is encouraging people to use the Nudge app, via Facebook and on iPhone and Android platforms, to lobby MPs and governments. Find out more at www.tearfund.org/app
