At the time of the 2010 general election, the Conservatives promised a transferable tax allowance worth around £150 to married couples.
The Liberal Democrat leader Nick Clegg ridiculed the proposals as "patronising drivel that belongs in the Edwardian age".
His party later secured a provision in the coalition agreement allowing them to abstain from voting on the issue.
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The Conservative peer said he was 'shocked' that the law had been vetoed by the Liberal Democrats.
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