The bank issued a statement after the Daily Telegraph newspaper said it was at the centre of a major investigation by HM Revenue and Customs (HMRC).
HSBC said it was investigating "an alleged loss of certain client data in Jersey as a matter of urgency".
HMRC said it had "received the data and we are studying it".
"We receive information from a very wide range of sources which we use to ensure the tax rules are being respected," the tax authority said.
In a statement, HSBC said: "Clamping down on those who try to cheat the system through evading taxes and over-claiming benefits is a top priority for us, and we value the information we receive from the public and business community."
Owning an offshore bank account is not illegal. But it is illegal to hide the interest which has accrued on the sums held, and to avoid paying tax on that interest to HMRC.
Geoff Cook, of the trade organisation Jersey Finance, said: "This is a serious matter and we note HSBC's immediate commitment to co-operating with any investigations carried out by the relevant authorities and welcome the clear position taken by the Jersey Financial Services Commission, that any failure to adhere to Jersey's clear standards will be robustly investigated and acted upon."
According to the Daily Telegraph, the tax authorities have obtained details of "every British client of HSBC in Jersey" based on information provided by a whistle-blower this week.
"These cases will be very complex, difficult and ultimately time consuming to unravel”
BBC business editor Robert Peston said: "It is really quite difficult to tell from this disclosure whether or not this is an example of HSBC yet again having, shall we say, laxer or weaker controls over who it takes money from.
"The American authorities do think HSBC was, for too many years, too prone, or in a sense, too easily duped by terrorists and criminals who wanted to launder money. We just don't have enough information whether or not this is an another example of those weak controls."
Our business editor said he had been told by HSBC that this appeared to be a case of "whistle-blowers handing over bunches of bank names for whatever reasons".
He added: "They don't think they will emerge from this investigation to be shown to be particularly lax in their controls."
Earlier this year, a US Senate report alleged that staff at HSBC's global operations had laundered billions of dollars for drug cartels and terrorists in a "pervasively polluted" culture that persisted for years.
The report detailed how HSBC's subsidiaries cleared suspicious travellers' cheques worth billions, and allowed Mexican drug lords to buy planes with money laundered through Cayman Islands accounts.
David Bagley, HSBC's head of compliance since 2002, resigned from his post when he appeared before the US Senate committee in July.
In theory, HMRC should know about most of the HSBC accounts already.
In 2006, it established a crucial legal breakthrough which meant, for the first time, that it could demand that banks reveal the identities of UK taxpayers who hold accounts offshore.
Since then, the Revenue has been sending demands to hundreds of UK and foreign banks, asking them to do just that.
This has already brought in several hundred million pounds in taxes, interest and penalties, from people who confessed that they had been hiding money abroad.
HMRC has received the latest list of HSBC accounts from the whistle-blower only very recently.
But even if it has come with names and addresses attached, it will not necessarily be an easy matter to identify the people who own the accounts.
Ronnie Ludwig, a tax partner at the accountants Saffery Champness, said some accounts were likely to be in the names of nominee companies and trusts, which hide the identity of the beneficial owner.
Some accounts could also have a trigger clause, he explained, which means the money is moved swiftly to accounts in other offshore tax havens, such as the British Virgin Islands or the Cayman Island, if HMRC intensifies its scrutiny.
Mr Ludwig told the BBC that even with an accurate list in its possession, HMRC would still have quite a task on its hands to sort through each account.
"HMRC is facing an uphill struggle in terms of its resources, because these cases will be very complex, difficult and ultimately time-consuming to unravel," he said.