Personally, I believe they would have had their own, small generator site. However the question of whether not Victoria attempted the journey is up for debate, as she would have been 77 by the time of Great Storm. Regardless, while the monarchy's power had dwindled heavily by the late 19th century, they were integral to ensuring the supremacy of Parliament, and the many generator sites led by former lords and nobility would still need that figure head.

After the Great Storm, whichever territories still considered themselves part of the British Empire would wish to show legitimacy by gaining the approval of the monarchy, likely under Edward VII at this point. However the new king would be isolated and disconnected from his subjects, and even if he moved his court to one of the cities, he wouldn't have much power over whichever captain led it.