The Home Secretary also said the party would honour its promise to hold an in/out referendum on EU membership after the next general election.
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The former England captain said he was "overwhelmed" by the messages he received from football fans after Rebecca died from cancer.
David Cameron said the measure, which will save £4 million by 2020, showed a commitment to his "all in this together" approach.
The party has dropped its opposition to an in/out referendum on EU membership and now supports a vote, acting leader Harriet Harman said.