Chris Williamson leaves his role as shadow fire and emergency services minister in what a source said was a "mutual decision" with the Labour leader Jeremy Corbyn to allow him to campaign on a broader range of issues.
Formally, councils in England have to hold local referendums if they wish to increase council tax by over three per cent in a year, although combined with a precept for local authorities providing social care, it is possible that council tax bills could increase by up to 5.99 per cent without a public vote.
The Derby North MP stepped down as shadow fire minister saying he wanted to campaign on a "broader range of issues".
Brandon Lewis, Tory Party chairman, said: 'Chris Williamson may have gone, but it remains Labour policy to hike council taxes massively.
Labour MP Wes Streeting said Mr Williamson should have been sacked "a long time ago" for his views on anti-Semitism.
Announcing 13 appointments, Mr Corbyn said: "I am pleased to make these appointments to strengthen Labour's frontbench team, which is now a Government in waiting".
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He added: "I know that on the backbenches, Chris will be a strong campaigner on a range of crucial issues as well as serving his constituents with dedication".
In August, discussing rows over Mr Corbyn's handling of anti-Semitism in the party, Mr Williamson told The Guardian: "Many people in the Jewish community are appalled by what they see as the weaponisation of anti-Semitism for political ends".
Williamson was one of Corbyn's most loyal supporters, regularly speaking out in defence of the Labour leader.
A key ally of Jeremy Corbyn has quit Labour's frontbench after making controversial comments on policy.
Williamon's call was not official Labour policy and Business Insider understands that senior party figures were unhappy with the publicity aroused by the idea.
But his proposal was immediately met with criticism and Tory MP Henry Smith said the proposals showed Labour was determined to put its "hands in the pockets" of hardworking households.