In a speech in London yesterday, Sir Jon voiced his belief that international authorities could not say with confidence now that they could resolve a failing global banking giant without public support, but flagged significant progress on measures to ensure banks had adequate capital and liquidity.
The deputy governor, who has responsibility for financial stability, said of the aim of ending a situation of institutions being too big to fail: "This may well be the litmus (test) by which the public judges the success of the entire reform programme.
"Nothing has so incensed public opinion and damaged societal support for the financial sector than the apparent 'heads I win, tails you lose' experience of private profits and pay when things went well and public losses (when) they did not."
He added: "We will not fully restore public confidence until we can show that we can resolve failing banks - no matter how large - without public support."
Sir Jon noted the UK, European Union, US and many other jurisdictions now had, or would soon have, legal powers to break up and wind up failing banks with "far less threat to the economy as a whole".
He added: "These powers include the ability to 'bail in' a bank's creditors, making them, not the taxpayer, responsible for a failed bank's losses once a bank's equity has been exhausted."
The UK taxpayer, at the height of the global financial crisis more than five years ago, had to put up tens of billions of pounds to rescue Royal Bank of Scotland from the brink of collapse and to back Lloyds TSB's rescue takeover of Bank of Scotland and Halifax owner HBOS.
Mulling whether the "too big to fail" problem had been solved, Sir Jon said: "We have made a lot of progress on too big to fail. But we are not yet there. I do not think we can say with confidence now that we could resolve a failing global giant."
He added that getting agreement on international standards to "end too big to fail" was perhaps the most important regulatory priority for the summit of the Group of 20 nations in Brisbane, Australia, in November.