Panorama has seen accounts from 106,000 clients in 203 countries, leaked by a whistleblower in 2007.
The documents include details of almost 7,000 clients based in the UK.
HSBC admitted that some individuals took advantage of bank secrecy to hold undeclared accounts. But it said it has now "fundamentally changed".
The bank now faces criminal investigations in the US, France, Belgium and Argentina.
HSBC said it is "co-operating with relevant authorities". But in the UK, where the bank is based, no such action has been taken.
At 15:30, there will be an urgent question in the House of Commons on tax avoidance by HSBC, tabled by Labour MP for Birmingham Ladywood Shabana Mahmood.
"We need to understand whether actually HMRC have been putting lots of cases before the Crown Prosecution Service (CPS) and it's the CPS who've been refusing to prosecute and those are questions that I hope that the government will answer," she said.
Offshore accounts are not illegal, but many people use them to hide cash from the tax authorities. And while tax avoidance is perfectly legal, deliberately hiding money to evade tax is not.
India's finance minister Arun Jaitley has said that all Indian names on the list will be investigated, although he cautioned that some accounts might be legitimate. A current inquiry looking into more than 600 people who hold accounts overseas, will now be widened to look into the the current list of names.