Labour has set out a series of measures it claims will "stop the super-rich hiding their wealth" in tax havens.
They include forcing transparency standards on UK overseas territories and a register of offshore trusts.
The party has called for a public inquiry into alleged abuses uncovered in leaked documents from a Panama law firm - and vowed not to accept donations linked to tax avoidance.
The government has set up a task force to look into the Panama Papers.
And the prime minister has taken the unprecedented step of publishing details of his tax and income over the past six years following Labour claims he had misled the public over whether he had benefitted from an offshore fund.
David Cameron will also host an international anti-corruption summit in London next month - and the government is to publish a register of beneficial ownership, revealing who ultimately gains from shadowy shell companies used to avoid tax.
But Labour argue Mr Cameron should publish his full tax returns and say the government's £10m task force must be "fully independent and in public".
Shadow chancellor John McDonnell said: "After a week of half-truths and spin from this government in the wake of the revelations in the Panama Papers leak, it's time to clean out the tax havens with real government action.
"It should be a matter of shame to the British government that more than half the companies recently named in the Panama Papers were registered in UK-governed tax havens.
"Not only has this government impeded international efforts to crack down on tax avoidance and to tackle tax havens but senior figures are personally implicated in these immoral schemes."
Other measures in Labour's "tax transparency" plan include:
- Changing the MPs' register of interests to include offshore holdings
- Doubling the number of HM Revenue and Customs staff scrutinising the tax affairs of wealthy individuals and companies
- Consider making foreign companies tendering for public sector contracts register in the UK for tax purposes
- Imposing greater transparency on multinationals and giving better protection to whistleblowers
- A crackdown on "accounting tricks" used to hide wealth
Labour also questioned a letter Mr Cameron wrote to EU officials in 2013, which called for offshore trusts to be excluded from a crackdown on tax avoidance.
The government said Mr Cameron had felt forcing trusts to reveal who gained financially from them would "distract" from action in more pressing areas.
But Mr McDonnell said: "It is deeply concerning that our prime minister has still failed to clarify whether or not he or his family were benefiting directly or indirectly in 2013 when he was lobbying to prevent EU measures to better regulate trusts as a way to clamp down on tax avoidance."
The shadow chancellor also promised that Labour would reject any donations linked to tax avoidance.
Political donations made by individuals are not tax-deductible in the UK - but money left in wills to major parties is not subject to inheritance tax.
Labour accepted a £1.65m donation in shares in 2013, from home shopping magnate John Mills, which he said at the time was a more "tax efficient" way of donating to the party than giving cash.
Quizzed about the Mills donation on BBC Radio 5 live's Pienaar's Politics, Mr McDonnell said: "Every penny that comes in to us will open and transparent.
"We will not be touching money that is used by any way in measures to avoid tax or evade tax, we will not allow that to happen and we're not allowing that to happen."
Mr McDonnell and Labour leader Jeremy Corbyn have also suggested that the inheritance tax system is in need of reform to make it "fairer".
Mr McDonnell told Pienaar's Politics: "I don't personalise politics, this is about the system, and a system whereby someone can inherit, effectively, £500,000 from his mum and dad and not pay a penny on it, I think there's something wrong in the system that allows that to happen."
But Housing minister Brandon Lewis pointed out that the gift from Mrs Cameron to her son was no different from similar arrangements used in other families, it was just a "larger sum of money".
Jeremy Corbyn has previously suggested the current 40% inheritance tax rate, which kicks in at £135,000, should be "graded" so the wealthiest families pay more.