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The decision to abolish the tax was announced by the Chancellor George Osborne in his emergency budget.
The landline duty had been proposed by the former government to introduce a payment from anyone with a fixed phone line of 50p a month to fund the improvements and expansion of the UK's broadband network.
The money would have been used to raise £170m to fund a superfast broadband, which will now be something that the private sector has to pick up.
Labour announced the plans and was on course to introduce them but it was postponed because of the general election and now the tax will never be introduced.