George Osborne said HSBC must deal with the "legacy of the past" as he indicated new laws could be needed to deal with tax evaders.
The Chancellor said he had been unaware of allegations that the Swiss arm of HSBC had colluded in tax evasion at the time its former chairman Lord Green was appointed as a trade minister.
Speaking on Radio 4's Today programme, Osborne said the Government was "looking at further changes to the law to make sure that we have a tough regime".
"If there are deficiencies in the law, if it's difficult to bring these prosecutions, then we should change the law," he added.
George Osborne has confirmed the Government is "discussing a plan" to give Greater Manchester control over its entire NHS budget.
The Chancellor called it "a very exciting development", saying: "We have a National Health Service, but we also want to have people in Manchester having greater control over their own affairs."
The Government has netted another £500 million from the sale of shares in Lloyds Banking Group, it was revealed today.
The transactions mean the UK taxpayer now holds a 23.9% stake in the bank, compared with 40% when it was bailed out during the financial crisis.
The amount of money recovered from the bank is now just under £8 billion after the latest round of share sales was launched in December.
Can confirm today that we have raised a further £500m for the taxpayer through Lloyds share sales, taking total recovered to £7.9bn
George Osborne insisted Britain remains "hugely influential in the world" after former Nato commander General Sir Richard Shirreff said the Prime Minister has become "a diplomatic irrelevance" over the Ukraine crisis.
Osborne was pressed repeatedly on BBC1's Andrew Marr Show over whether the Ministry of Defence's share of the cuts would mean falling below the commitment of at least 2% of national wealth going to the military
"We are currently hitting that target. I am not going to pre-judge our defence review. But people know that we care about our nation's security and defence because we have invested in the latest equipment," Osborne said.
"People know we have met the 2% commitment and are meeting it today."
George Osborne has confirmed the Government is extending the pensioner bonds scheme for a further three months "so potential savers don't miss out".
The Chancellor wrote on Twitter:
Our 65+ pensioner bonds have been most successful saving product ever – over 7.5bn bonds have been sold to over 610,000 pensioners so far
Confirming today that the 65+ bonds will be on sale until 15th May - so potential savers don’t miss out on the market-leading rates on offer
George Osborne said he believes a Greek exit from the eurozone would have "very serious consequences."
The Chancellor told the BBC's Andrew Marr Show, "This stand-off between Greece and the eurozone is increasing the risk every day to the British economy."
"Greece has worked hard to stay in the eurozone, and frankly a Greek exit from the eurozone in my view would have very serious consequences," Osborne said.
"We've got to avoid this crisis getting out of control," he added.
Greek finance Mmnister Yanis Varoufakis promised that his country will "never again" have a budget deficit and tried to reassure Germany that Athens' new policies did not mean it was turning its back on reform.
Varoufakis told German newspaper Die Zeit:
The Germans have to understand that it doesn't mean we are straying from the reform path if we give a pensioner who lives on 300 euros a month an extra 300 euros a year.
I can promise you Greece will - apart from interest payments - never again present a budget deficit. Never, never, never!
Varoufakis added that the new Greek government "will never seek financial help from Moscow."
He is scheduled to meet German Finance Minister Wolfgang Schaeuble tomorrow after touring Europe to drum up support for plans to halt the austerity policies prescribed by Berlin.
The stand-off between Greece and the eurozone is fast becoming the biggest risk to the global economy, George Osborne has said.
The Chancellor made the comment after meeting with Greece's new finance minister Yanis Varoufakis.
Osborne said he had told Varoufakis that all sides on the debate about Greece's debt need to "act responsibly".
Greek Finance Minister Yanus Varoufakis has arrived at Downing Street for his meeting with Chancellor George Osborne as he attempts to strike a new deal for the struggling nation.