Labour's non-dom policy was a centrepiece of the election campaign - promising to use the £1bn a year proceeds to fund NHS and dental appointments, and school breakfast clubs.
Chancellor Rachel Reeves committed to ending the "loopholes" again in Liverpool this week at the party's annual conference.
Prime Minister Sir Keir Starmer said they are doing it because "those with the broadest shoulders should bear the heavier burden". The pain on the way being shared equally.
But now it's claimed Ms Reeves may water down the crackdown amid concerns the policy will not make as much money as had been expected.
There are said to be concerns the Office for Budget Responsibility, which independently scores every policy, will say it will raise far less than was suggested - if anything at all.
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"Non-dom" is short for "non-domiciled individual" and refers specifically to the tax status of a person who is a UK resident but whose permanent home is abroad.
The Treasury would not comment on budget speculation - but said it was committed to ending the "outdated" non-dom tax arrangement and attracting talent and investment to the UK. Labour's budget is set to take place on 30 October.
After former chancellor Jeremy Hunt removed non-dom tax breaks in his final budget in March, Labour insisted they would go further - with a "full fat" rather than "semi-skimmed" version, a source said.
The loopholes they identified were axing a 50% tax discount in the first year, intended to encourage investment; and making money stashed in trusts liable for UK inheritance tax.
Wealthy non-doms moving abroad
Experts have warned in meetings with the Treasury these are already leading wealthy non-doms to move elsewhere.
Lesley Macleod Miller, head of Foreign Investors for Britain, which has commissioned research into the policy, told Sky News: "We are very heartened that the Treasury appears to be listening.
"Our research shows that rather than making money, the exchequer will lose up to £1bn per annum for generations. This will create a further hole in addition to the £22bn hole the government already has.
"They need to understand that these people can be anywhere. They can be in Switzerland, they can be in Italy, they can be in Greece. And those countries are saying 'if you are not welcome in the UK, come to us, bring your investments'."
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Arun Advani, director of the Centre for the Analysis of Taxation and an associate professor of economics at the University of Warwick, said many would not desert London, where almost all non-doms are, because of its financial sector.
But he added that the cliff edge on paying inheritance tax in full after 10 years could be eased to keep them here long-term. "After nine years and 364 days, you suddenly pay 40%, that may scare a few people."
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Tap hereTaxing non-doms has become an article of faith for the new government.
But with anger over the removal of winter fuel allowance from all but the poorest pensioners, the budget is a key moment to show is pain is being shared fairly.
Ministers will need to tread carefully.
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