The UK government currently owns 84% of Royal Bank of Scotland
Measures to prevent taxpayers from ever having to bail out banks again have been discussed at a meeting chaired by the City Minister, Lord Myners.
The peer met officials from financial institutions and the world's richest countries.
He said if banks fail in the future then their owners should pay the price.
One of the items on the agenda was whether banks or insurance companies should pay an insurance levy to cover the cost of any future bail-out.
"We have [made progress] talking about specific issues relating to how we make the system for world banking more resilient in the future than it has been in the past," Lord Myners told BBC Radio 4's PM programme.
David Buik on UK and US banking plans
"In particular to make sure that if banks fail in the future, the cost of that failure is fully and completely borne by banks and their shareholders, and never again falls on the world's taxpayers."
Officials from each of the G7 nations, as well as the World Bank, International Monetary Fund, Bank of England and Financial Services Authority, attended the seminar at 11 Downing Street.
The meeting followed US President Barack Obama's announcement that he will impose a levy on American-based banks to repay the billions of taxpayer dollars spent bailing the sector out.
At last year's G7 summit in St Andrews, Gordon Brown suggested the introduction of a transaction tax, although Lord Myners said that this was not discussed at Monday's meeting.
A possible global agreement on how to prevent future bank bail-outs is very much in its early days with different countries having different approaches, BBC business editor Robert Peston says.
"When it comes to tax, getting ministers to agree is harder than herding cats," he said.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.