It may force new elections, I don't know that the outcome would be a foreordained conservative led government.
The Conservatives were however, pretty much unconditionally pro-Entente, and anti-German, along with several of the press barons. So if they stick with that, and get into power, Britain is going to war, just later, unless they are breaking campaign promises. I was tempted to say that bringing Britain into the war a few weeks late would mean bringing Britain in just in time to lose. However, on reflection, that really wouldn't be the case in an east first scenario, because any defeats of the French would be defeats of French offensives, not the conquest of France by German invasion, which was the threat in OTL 1914.
By the end of 1914, no matter what Britain has done, the Austrians are likely to have have taken Belgrade and most of Serbia, and the Germans are likely to have pushed the Russians out of most of Congress Poland. The Austrians are likely to have basically held their Galician border. The Germans are likely to have basically held their Alsace-Lorraine border. So, the Entente powers (either France and Russia, or France and Russia plus Britain) will have a long slog ahead of them of them if they want to bring down the Central Powers, or even push back to the status quo ante bellum. Likewise, to impose a true victor's peace or destroy either Russia or France as great powers, the Central Powers would have a long, daunting slog ahead of them. However, of the two coalitions, the CPs are the better positioned to take and hold their winnings and declare, "Yay, we win on points, ready to make a deal now, or would you like to suffer some more beatings as you try and fail to take your territory back and resuscitate your little terrorist sidekick?"