During the Civil War in OTL, the U.S. was able to build a Monitor class vessel in three months. And this was building them from the keel up...the Eads ironclads (conversioins of existing ships) took even less time. The British would not be able to easily duplicate that. And it has to be remembered that Britain will have to build OCEANGOING ironclads...a much more expensive and complicated type of vessel to build...if it wants to fight in American waters (for example, to maintain a blockade). All the U.S. has to build are coastal vessels capable of breaking the blockade. So I think, in the long run, Britain loses the naval war, too.
It must also be remembered that a moniter has 2 guns vs 44 of HMS Warrior and even vs the larger american costal ironclads you are talking about a ship with double their armourment. Also factor in the possibilty of conversions of old 1st rates (>90 guns) even with a reduction to take into acount the armor you are still talking about 60-80 heavy guns.
In order to break a blockade by such vessels the US would need a comparable fleet which they simply cannot build in time, hence the US remains under blockade and its economy dies.
Conclusion: Even if the US manages to take Canada it is still doomed reguardless.
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