This week's featured article at the Sobel Wiki is on Great Britain.
Sobel's focus on the Confederation of North America and the United States of Mexico means that Great Britain becomes steadily less important to the story as the narrative moves away from the point of divergence in 1777 and the C.N.A. gains steadily more autonomy through the 19th century. Among other things, this means that we have no idea whether Ireland was united with Great Britain as it was in our history in 1800. Given that the American and French Revolutions were unsuccessful, and given the example of the C.N.A. as a British possession with an autonomous government, it is possible that Ireland would have retained its own Parliament into the 20th century.
Another issue Sobel glosses over are diplomatic relations between Great Britain and the C.N.A. Given that the C.N.A. is basically a larger version of our own history's Canada, it's useful to use Anglo-Canadian relations as a basis for comparison. Our own history's analogue to the drafting of the Second Britannic Design was the Confederation of 1867. Following Confederation, Canada's first Prime Minister, John A. Macdonald, sent an unofficial envoy to represent Canada in London. In 1880, the office of Canadian envoy to Britain was formalized under the name High Commissioner, and this set a precedent for diplomatic envoys between Commonwealth nations.
Sobel makes no mention of a formal North American envoy to London after passage of the Second Britannic Design in 1842. However, he does mention that Governor-General William Johnson sent his Minister of State, Montgomery Harcourt, to London in 1853 to seek increased British investment in the C.N.A., which suggests that there was not a regular North American diplomatic mission in London at the time, though the C.N.A. did have its own Office of State, and presumably maintained diplomatic relations with other nations, especially the U.S.M. By contrast, Canada did not have an equivalent government department until 1909, and since the Canadians wanted to avoid calling it the Foreign Ministry (since Canadian foreign policy was still controlled by the British government), it was called the Department of External Affairs, and Canada didn't begin establishing formal diplomatic relations with other countries until the 1920s.
By the time the Global War broke out in 1939, Great Britain had a regular diplomatic mission to the C.N.A. headed by an ambassador (and vice versa, presumably). Given Ezra Gallivan's isolationist foreign policy, including his desire to distance the C.N.A. from Great Britain, it is likely that this dated from his administration in 1888 at the latest.
At the end of For Want of a Nail, Sobel speculated that in the future, the C.N.A. might form a union with the United British Empire, or even that Great Britain might join the C.N.A. as a new confederation.