No, British Prime Minister is not facing a vote of no-confidence, although his back-bench MPs risked their political careers making known their outrage:
They want the UK out of the Eurozone.
With the looming collapse threatening the Common Market, the British public are growing weary of their attachment to the Continent's financial misfortunes. They have long opposed casting aside the British pound, still trading higher than the Euro and the U.S. dollar despite the anemic global economic recovery. Why be half wedded to a spouse so dissolute and extravagant that she cannot pay her own way for anything?
The European Union has done very little to resolve the very nettlesome controversy that impedes any general economic policy: nation-states. France, Spain, Germany, and all the other seventeen member-states under the Euro-umbrella will not acquiesce to a common economic policy in line with trading on the same currency. Nations do not give up their identity, their pride, or their power absent military surrender or insurmountable crisis.
Perhaps former Prime Minister Margaret Thatcher's prophecy concerning the short life of the Euro is coming to pass. Then again, if the toxic debt poisoning the Euro through the Mediterranean member states triggers a continental resolve, then the pesky matter of nation-states will give way to the collective will of one government overseeing one currency.
Whatever the outcome on the Continent, it remains in the best interests of the United Kingdom to withdraw as soon as possible from the Eurozone, now growing into a maelstrom-sinkhole sucking away the political and economic liberty of every nation-state connected with it.