Some power-players in the British government in the 1830s-1840s
were interested in buying California from Mexico in exchange for money that Mexico owed to the United Kingdom IOTL (source:
here), though a change in administration in the United Kingdom and the Texan rebellion in Mexico prevented it from taking place. And it was so far away that it wasn't impossible for the British to colonise it; they managed Australia, after all, and it's not as if there was a large American presence in the territories immediately to the east (California achieved the necessary population to get statehood quite a while before all the territory between it and the east coast did). The problem with this counterfactual is that the Americans will probably not take kindly to a strong British presence in California, especially with the whole 'from sea to shining sea' thing.
A secession of New England (which really
wasn't just hot air, by the way—true, supporters of outright independence were on the fringes of the movement, but so were supporters of outright American independence even into the American Revolution until their appeal to the King to override Parliament was rejected, and the American government was unlikely to be conciliatory toward them; they were only discredited by the timing of their political action with the United States coming out surprisingly well from the War of 1812) is probably necessary to weaken the USA enough for the British to plausibly hold California; New England held much of the United States' commercial and industrial power, so without it the United States' position in North America
vis-à-vis the British Empire is much less overwhelming.
In a map game I had California be successfully acquired by the British Empire (and thus end up in Canada) by the annexation happening during an (earlier-than-OTL) American Civil War, so it was a
fait accompli by the time the USA was free to do anything about it… but that wasn't exactly hard AH.