On 3 September 1939, the United Kingdom declared war on Germany. The Canadian Parliament was 
called in special session and both Prime Minister William Lyon Mackenzie King and opposition leader Robert Manion stated their support for Canada following Britain but did not declare war immediately, partly to show that Canada was joining out of her own initiative and was not obligated to go to war. After two days of debate, the House of Commons approved an Address in Reply to the Speech from the Throne on 9 September giving authority to declare war to King’s government. A small group of Quebec legislators attempted to amend the bill, and CCF party leader J. S. Woodsworth stated that some of his party opposed it. Woodsworth was the only Member of Parliament to vote against the bill and it thus passed by near-acclamation.[14][15] The Senate also passed the bill that day. The Cabinet drafted a proclamation of war that night, which Governor-General Lord Tweedsmuir signed on 10 September.[16] King George VI approved Canada’s declaration of war with Germany on 10 September.
At the outbreak of war, Canada’s commitment to the war in Europe was limited by the government to one division, and one division in reserve for home defence. Nevertheless, the eventual size of the Canadian armed forces greatly exceeded those envisioned in the pre-war period’s so-called mobilization
“schemes”. Over the course of the war, the army enlisted 730,000; the air force 260,000; and the navy 115,000 personnel. In addition, thousands of Canadians served in the Royal Air Force. Approximately half of Canada’s army and three-quarters of its air-force personnel never left the country, compared to the overseas deployment of approximately three-quarters of the forces of Australia, New Zealand, and the United States. By war’s end, however, 1.1 million men and women had served in uniform for Canada. The Navy grew from only a few ships in 1939 to over 400 ships, including three aircraft carriers and two cruisers. This maritime effort helped keep the shipping lanes open across the Atlantic throughout the war.
While the response to war was initially intended to be limited, resources were mobilized quickly. The Convoy HX-1 departed Halifax just six days after the nation declared war, escorted by HMCS St. Laurent and HMCS Saguenay.[23] The 1st Canadian Infantry Division arrived in Britain on 1 January 1940.[24] By 13 June 1940, the 1st Battalion of The Hastings and Prince Edward Regiment was deployed to France in an attempt to secure the southern flank of the British Expeditionary Force in Belgium. By the time the battalion arrived, the British and allies were cut off at Dunkirk, Paris had fallen, and after penetrating 200 km inland, the battalion returned to Brest and then to Britain.
Apart from the Dieppe Raid in August 1942, the frustrated Canadian Army fought no significant engagement in the European theatre of operations until the invasion of Sicily in the summer of 1943. 
With the Sicily Campaign, the Canadians had the opportunity to enter combat and later were among the first to enter Rome.
For just over 2 years, the Canadian Army in the U.K. waited… waited and trained. With the war raging on the continent and in North Africa, why did the Canadians remain in the U.K.?
It is possible that the British did not want Canada to send troops in 1939. Canada’s primary role was to train pilots from throughout the Empire with the British Commonwealth Air Training Plan, which the British proposed on 26 September 1939, and supply food and raw materials, not send hundreds of thousands of troops overseas as it had done in World War I. Canada fully cooperated with Britain otherwise, devoting 90% of the manpower of the small RCAF to the air training plan; a force that had trained 125 pilots annually when the war began now produced 1,460 airmen every four weeks under the plan.
Between the collapse of France in June 1940 and the German invasion of the USSR in June 1941, Canada supplied Britain with urgently needed food, weapons, and war materials by naval convoys and airlifts, as well as pilots and planes who fought in the Battle of Britain and the Blitz. During the Battle of Britain between 88 and 112 Canadian pilots served in the RAF,[30] most had come to Britain on their own initiative. For political necessity, an “all Canadian” squadron was formed under the British Commonwealth Air Training Plan at the start of the war and the Squadron served in the Battle of France. They were later joined by No. 1 Squadron RCAF in June 1940 during the Battle for Britain and they were in “the thick” of fighting in August, by the end of the battle in October 1940, 23 Canadian pilots had been killed.
The Canadian army remained, in the main, in the U.K. until the invasion of Sicily in July 1943.
Reference: https://en.wikipedia.org/wiki/Military_history_of_Canada_during_World_War_II