Ministers have warned David Cameron to resist a "lurch to the right" after the Conservatives finished third behind UKIP in the Eastleigh by-election.
David Cameron is also facing pressure over departmental spending and the welfare bill ahead of this month's Budget.
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Thames Valley Police named the victims as Savaan Mundae, Jaspal Bahra, Thanh Nguyen and Captain Michael Green.
Mild & wet with winds whipping up
The Chancellor said he will use the Budget to "invest to secure a bright future", in a signal he is ready to usher in the end of austerity.