According to a dubiously cited wikipedia article, the allies' objectives for intervening in the Russian Revolution was:
Faced with these events, the British and French governments decided upon an Allied military intervention in Russia. They had three objectives:^([4][better source needed][not in citation given])
- prevent the German or Bolshevik capture of Allied material stockpiles in Arkhangelsk
- mount an attack helping the Czechoslovak Legions stranded on the Trans-Siberian Railway^([not in citation given])
- resurrect the Eastern Front by defeating the Bolshevik army with help from the Czechoslovak Legions^([not in citation given]) and an expanded anti-Bolshevik force of local citizens and stop the spread of communism and the Bolshevik cause in Russia.
Is this accurate? If so, why did the Allies continue supporting the White Army after Russia signed a separate peace with germany, if the only reason for their involvement was due to the war effort?
Please correct me if I'm wrong, but wasn't the Russian Monarchy a historical enemy of England?
No, there was no real support for the Russian monarchy - in fact, the Entente nations eagerly welcomed the Liberal-Socialist Provisional Government that replaced it in the March Revolution. Not only was it much more in-line with the Western democracies, it also removed a chief German allegation that the Allies could not really be fighting for democracy if one of their main warring partners was itself the most autocratic nation in Europe. You seem a little confused. There were two Russian revolutions, the one in March which forced the Tsar to abdicate, and a Bolshevik one in October. The Entente supported the March revolutionaries and did not support the Bolsheviks. The Provisional Government continued fighting on the Allied side, while the Bolsheviks made a separate peace with the Central Powers in 1918, breaking their commitment to the Treaty of London, and also repudiating Russian government debts.
I think your question, then, is built on a false premise. Yes, those war aims are correct for why the Allies supported the Whites. It was the Bolsheviks who dropped out of World War I, not the March revolutionaries who replaced the Tsar. The Whites promised to honor Russia's obligations to remain in the war and continue to fight the Germans on the Eastern Front. This was obviously of crucial importance to the Allies, otherwise thousands of German and Austro-Hungarian troops could transfer to the Western Front, and the Central Powers could make use of food and resources in Russia. The Allied intervention had more to do with fighting World War One than reversing a revolution in Russia. Most Allied officers believed the Bolsheviks to be German agents and made no differentiation between the Germans and the Reds.
The White movement was not an inherently monarchist organization. It is difficult, nevertheless, to make sweeping statements about it, because rather than a coherent political force the Whites were a loose confederation of anti-Bolshevik governments and warlords spread all around the fringe of the Russian empire, with political convictions ranging from ultra-monarchist to liberal to agrarian socialist. In fact, even though many White officers may have been monarchists, the most important White leaders, Admiral Kolchak and General Denikin, both promised to support the liberal Constituent Assembly government of Russia and had no desire to re-instate the Tsars. The Russian monarchy ceased to be a political factor in March, even before they were put up against a wall in Ekaterinburg.