Through the 19th century, American trading vessels were unmolested by the British Navy ONLY because it was made clear the USA would retaliate by invading (and seizing) Canada.
Also, do not forget the British involvement in our Civil War (aiding the Confederacy).
The British were not involved in the Civil War and they did not aid the Confederacy despite their desire to trade for cotton.The British Parliament declared neutrality and 40,000 Canadians fought for the blue and the grey, mainly for the North.