Were they anxious about fighting on the side of the largest Communist power? Were they overjoyed at the new ally? Did Churchill/the parliament see eventual war with the USSR coming once Germany had been defeated? Did they even hope for the USSR's defeat by Germany?
"If Hitler invaded Hell, I would at least make a favourable reference to the devil in the House of Commons." Churchill, To his personal secretary John Colville the evening before Operation Barbarossa
Churchill had been an arch anti-communist ever since the revolution. He had been the driving force behind the Western Allies sending troops to fight the Bolsheviks during the Russian Civil War in 1919-22; he really really wanted to send troops to Finland in 1939-40 to fight the Soviet invasion and had to be talked out of violating Norwegian and Swedish neutrality to get them there. Churchill made Joe McCarthy look like a wishy washy pinko liberal. Churchill also knew that the Americans were still showing no signs of wanting to get involved, and that Britain couldn't fight on alone indefinitely. He knew that the Germans would have to abandon any idea of invading the UK if they were fighting in Russia. As the quote suggests, if he was an arch-anti-communist, he was also an arch-pragmatist (as he'd already shown with the Mers-el-Kebir incident).
"The Russian danger is therefore our danger and the danger of the United States just as the cause of any Russian fighting for his hearth and home is the cause of free men and free peoples in every quarter of the globe."
Churchill, June 22nd, 1941.
Full speech (and even audio sample) can be found here.
While people think about how to answer this question, I'd like to point out that the USSR's entrance into World War II was not the German invasion of the Soviet Union in 1941, but the Soviet invasion of Poland in 1939.