The Peninsular War, Napoléon still needs to stabilizes Spain and deal with Portugal, and Iberia does not get anywhere near as cold as Russia. Once Iberia is stabilized the British Asian trade is drastically hurt as they now sail around the Cape of Good Hope. In America we have the War of 1812 still happening, and with Napoléon still a threat Britain is going to be more concerned about Europe which means less resistance for the US. Which just leaves the African Colonies.
Anyway consider this a two POD question, no Russian Campaign and a more effective Continental System, the main question is if Britain did surrendered due to exhaustion could Napoléon divided the country?
Have fun in Portugal. My point is that Napoleon needs a target he can get to more easily than the British can. Iberia is not it, Italy is not it, the Balkans are not it.
I will take it you mean something like Cape Finisterre rather than the Cape of Good Hope. The thing being the British did do precisely that. The Continental System leaked because no one could stop British ships getting into harbours even in the ports of compliant countries let alone interdict British convoys at sea.
However even assuming some brilliant world shattering success against the Lines of Torres Vedras and Gibraltar both Britain is not going to surrender. They may find revenues drop sufficiently that they need to come to terms but that is a long way short of surrender.
The concise answer to the question can Napoleon break Great Britain and Ireland up into separate kingdoms is no. The longer answer includes the point that Napoleon's army is stuck the wrong side of the water for a very long time. The British could easily hold America off with the troops they could spare from the Peninsula Campaign (it was attacking that needed more troops it generally does) and their fleets still control the oceans of the World. Just bilateral trade with India pays an awful lot of salaries.
The best Napoleon can hope for is a repeat of something like the Peace of Amiens while both sides take stock as pointed out by Unprincipled Peter above and he does not even agree with me that Nappy is just bellicose megalomaniac with a passion for collecting countries, okay maybe I am being a bit harsh, the point there is a lot of pressure on the man requiring him to be seen to do something politically. A peace would do, a war that promised peace would do, an effort at slow strangulation where the other side were not the ones getting strangled is less effective and upsets people.