The first serious attempt to find a way from Europe to the “Indies” began with John Cabot in 1497, when he landed at what is now St. Johns, Newfoundland. Britain initially supported these explorations to avoid conflicts with the more powerful navies of Spain and Portugal. While this threat was gone within a half-century, English-led explorations continued nearly 400 years until the end of the 19th century.
Geographically, there is a passage through the Canadian Archipelago. The problem was that parts could be blocked by ice year-round. At best, navigation is through a transcontinental maze of islands to find open, ice-free water.
It was not an Englishman who made the first successful passage. The great Norwegian explorer Roald Amundsen did it in 1903–06. But it was not until 1944 that anyone crossed it in one season. That trip was made by Captain Henry Larsen in the Royal Canadian Mounted Police schooner St. Roch.