Speaking as a native English speaker from London: I can assure you that most Brits would get this question wrong. It is true that Brits use "jolly" to mean "very" but it is, as you've noted, informal. Brits do not use it this way in formal speech. You would have to make it clear in the question that you were talking about informal English. E.G. "Name a word that means 'happy' and can also informally mean 'very'".
Note that the question is never a single example or definition, but a starting question plus multiple clues and hints. These help to clear up ambiguities and guide the student towards the correct puzzle answer.