"Jolly good" meaning "extremely good" in British English
Solution 1:
- The word jolly has fourteen OED adjectival senses plus some sub-senses. Adverbially, it is sense 2a which you are discussing here:
2a. Qualifying an adj. or adv.; orig. appreciatively, then ironically, with intensive force: Extremely, very. Now colloq.
Examples of this sense were present from the 16th century:
1549 Coverdale et al. tr. Erasmus Paraphr. Newe Test. II. Phil. iii. f. viiv, I thought my selfe a iolye fortunate man [L. pulchre mihi videbar felix], aswell for the nobylitie of my kyndred..as also for my strayte obseruyng of ye law.
The essential difference between this way of using jolly and bloody is that the latter, a much stronger intensifier, is a swear-word, and considered offensive in some circles.
The word is never used that way in AmE. It is rarely used at all in AmE even as an adjective except in collocations with respect to Santa Claus and related Christmas things. (point 3 contributed by @Mitch, by way of edit)
Solution 2:
'Jolly' - is an intensifier. Although it is used today in the UK with simple and non-ironic intent ('that's jolly nice of you...'). It is also used in theatre/comedy to flag a particular class of (ridiculous) cholmondley-warner-ish Englishness.
Bloody - is also an intensifier, cruder and without the cultural baggage. Bloody is very common and relatively classless.
According to the OED both jolly and bloody have been used as intensifiers since the mid-1500s.