The government will "sweep away" tax secrecy by forcing so-called shell companies to declare who makes money out of them, David Cameron has said.
The prime minister told the Guardian that "secretive companies in secretive locations" were used to avoid tax.
He has also met the leaders of Britain's Overseas Territories and Crown Dependencies to urge them to be more open about their tax affairs.
Tax evasion and avoidance will be discussed at the G8 meeting next week.
Ahead of the G8 in County Fermanagh, the government has announced plans to require all British firms by law to register details of their ownership and beneficiaries with Companies House.
The register would be available only to authorities such as HM Revenue and Customs in the first instance but the government would consult on making it public.
Mr Cameron said he would like the register to be available to everyone but added: "I do not want to disadvantage Britain by doing something others won't do."
At the heart of the tussle is a perpetual tension. Governments want to secure what they believe they are owed, but also hope to secure a competitive advantage over others by offering tax incentives to firms in the hope of luring them to their shores.
That is the big picture. The detail breaks down like this: David Cameron wants to be seen to be getting his own house in order first, and so wants British Crown Dependencies to be much more transparent.
He also wants UK registered companies to be forced to be more clear about who their financial beneficiaries are. But he is not certain yet that such a register should be public.
Why? Because if other countries didn't follow suit, it could put British businesses at a disadvantage.
"The goal here is to have an international tax system that ensures that there aren't places where secretive corporate structures can hide their money from the tax authorities," he said.
"It's critically important that we have transparency about who owns companies and who are the ultimate beneficiaries of any given corporate structure."
Mr Alexander said such transparency would be "very powerful" and would enable the government to recoup more tax.
Alongside the new register, the government is also continuing to push for automatic information exchange with Britain's Overseas Territories and Crown Dependencies.
Bermuda, the British Virgin Islands, the Cayman Islands, Gibraltar, Anguilla, Montserrat, the Turks and Caicos Islands, Jersey, Guernsey and the Isle of Man were all represented at Saturday's meeting at No 10.
Many of the islands and outposts are regarded as tax havens, although that is a label they strongly dispute.
Richard Murphy, director of Tax Research UK, told the BBC how automatic information exchange would work.
"If, for example, you had an account in Jersey... Jersey would have to tell the UK you've got it and how much income you earn on it automatically, without your consent."
But he added: "Let's be honest, tax havens deliberately disguise who has accounts in their jurisdictions, whether that is individuals by some form of banking secrecy or companies through the use of trusts and offshore companies."
Jersey, Guernsey and the Isle of Man have already agreed to some information sharing with the UK, but not all other countries.
The prime minister will urge the leaders to sign up to the Multilateral Convention on Mutual Assistance in Tax Matters - an initiative led by the Organisation for Economic Cooperation and Development (OECD).
Bermuda said on Thursday it had agreed to back the OECD treaty, which is already signed by more than 50 countries.
Speaking in Downing Street, Jersey's Treasury Minister Philip Ozouf told the BBC there were a lot of "myths" about Jersey and the meeting was "an opportunity to explain what is not happening".
"Jersey is not a tax haven. We're certainly [ahead] of many other leading nations of the world in holding information and sharing it as appropriate with authorities about who actually owns Jersey companies...
"We're part of the solution, we're not the problem. We've got a responsibility to explain to MPs, to leaders around the world how good and beneficial some aspects of what happens in the well regulated, reputable financial centres such as Jersey are."