I don't think an occasion ever came up for a conquest. British-Danish relations were usually stable over the centuries. By the time Britain became overpowering, there was little friction between nations. The worst case of friction usually came due to Danish neutral trade with their enemies during wars (Napoleonic wars, 7 Years War) but Britain was usually a little busy at these times to conquer Norway. Also, I'm not sure if Britain had the firepower to conquer anything until around 1700. The Danish Navy was historically strong. Plus, one also had to worry how Sweden or/and Russia would think of the matter. Maybe their agreement might be gained by eliminating the sound tolls.
More likely is a personal union via dynastic marriage.
The absolute last chance of unifying crowns would be the Napoleonic Wars.
Norway was stripped from Denmark (largely as punishment for siding with France) and handed to Sweden. If Sweden hadn't switched sides and stayed loyal to France as well, then perhaps it would have been given to the King of England, not necessarily England itself. Very unlikely. Norway might have agreed if it was assured they'd have their own functional Parliament and would not be Britain's subordinate.
Parliament was always resentful of the perceived costs of helping the Georgian Kings keep their ancestral duchy of Hanover safe and were jealous of their kings time with other domains. However, Norway was still Britain's primary source of timber all the way to the age of steam and a joint crown might have been viewed in more positive light by the people as this was a strategic necessity and would open new markets there were highly protected by Danish tariffs.
Other than that, then the son of Queen Anne surviving and uniting the thrones of Britain and Ireland to Denmark-Norway in Personal Union in the same manner than Britain and Hanover were united in Personal Union by the Georgians. Either way, there would be significant friction between countries that the monarchs would have to constantly address. Hanover was a 3rd rate power. Denmark-Norway would demand far more of the King's time. It is possible a monarch may be forced to abdicate one or the other throne to a sibling of 2nd son.
There should be a timeline on this. Maybe I'll write one someday.