"Vapourise" or "vapourize" does seem to be considered an incorrect spelling of this word in any form of English. To understand why, you need to know a little bit about the history of words spelled with ⟨our⟩.
⟨or⟩ normally occurs in the spelling of Latin, as opposed to French, roots
Many Latinate words came into English from French (by which I mean, not modern French, but the Anglo-Norman dialect that was spoken by French speakers living in Great Britain).
The British English practice of using the spelling ⟨our⟩ in some words where Americans use ⟨or⟩ usually reflects the phonetic development of Latin "or" to French "our" (in Modern French, as Peter Shor mentions in a comment, the "ou" has often changed further to "eu"). Therefore, in words that are taken directly from Latin (or at least, treated as if they were taken directly from Latin), without the intermediary of French, we would generally expect to see ⟨or⟩ instead of ⟨our⟩.
⟨or⟩ is used before suffixes that strongly prefer to come after Latin roots (-ation, -ious)
Certain suffixes, such as -(a)-(t)-ion, strongly "prefer" to come after Latin roots. So for example, corresponding to the verb destroy (which shows some French sound changes) we have the noun destruction (which preserves the Latin spelling of the root). Another example is deceive, deception. The spelling difference between colour, coloration parallels the audible difference for some other sets of words; hopefully this is helpful for remembering it.
The Latin spelling ⟨or⟩ is also used in general before the suffix -ious, which explains labour vs. laborious.
⟨our⟩ is used before inflectional suffixes (-ed, -ing) and suffixes that strongly prefer to come after whole words (-hood, -ship, -ment)
Other suffixes, such as all English inflectional suffixes, can come after complete English words of any origin (and they can't come after Latin roots unless the root can be used as an independent word). Inflectional suffixes for verbs include -ed, -(e)s, -ing; so we write the inflected forms of destroy as destroyed, destroyed, destroying. In this case, destructed does exist, but it's the past tense of a different verb, to destruct. And we can only say deceived, deceives, deceiving: there isn't any such word as *decepted (which would be the past tense of a hypothetical verb to *decept). Likewise, ⟨colored⟩ would only make sense as the past tense of a verb to ⟨color⟩, which does not exist in the type of British English you're talking about.
Native English derivational suffixes such as -hood, -ship and -ful also fall into this category. So there is no change between neighbour and neighbourhood, saviour and saviourhood (or saviourship), or colour and colourful. In addition, the derivational suffix -ment, which comes from French, generally comes after a stand-alone verb, not a bare Latin root (so Collins gives discolourment, from to discolour, and marks discolorment as an American spelling).
Fowler (1926; repub. 2009) also mentions -ist and -ite as suffixes in this category. Labourist, behaviourist, colourist all prefer
⟨our⟩ in British English. However, florist does use Latin ⟨or⟩, as does arborist, from Latin arbor. Interestingly, humorist seems to be more common than humourist in British English (although both exist); see the Google Ngram Viewer and the British National Corpus (which has "humorist" with a frequency of 15, vs. "humourist" with a frequency of 4). I don't think -ite is really common enough to be worth worrying about, but the example Fowler gives is "Labourite".
Of course, words that are standardly spelled with word-final ⟨or⟩ in British English will keep this spelling when suffixed: motorist < motor, terrorist < terror.
Either ⟨or⟩ or ⟨our⟩ seems possible in theory before the suffix -able, but the standard spelling is currently ⟨ourable⟩
Some other suffixes, such as -able, behave both ways, and can come after either a whole word of any origin, or a Latinate root. This suffix did exist in Latin, and it can be used in English after Latin roots (although for some words the spelling may change to -ible) as in destructible. However, -able is also highly productive after regular English verbs of any origin, so we also can say destroyable (even if some people might consider it less elegant). In some cases, we don't even use the word formed from the Latin root, only the one formed from an English verb (we say deceivable, not deceptible). I think this explains why both favourable and favorable are possible in principle (to find out which is actually used more, it's necessary to consult a dictionary or corpus of British English).
Fowler advises ⟨our⟩ before -able, and this is backed up by a look at the Google Ngram Viewer for "colorable" vs. "colourable" in the British English corpus.
⟨or⟩ is usual before the suffix -ise/-ize, which prefers to come after Latin roots (although it can also come after English words)
The suffix -ize/-ise is Latinate, and often prefers to come after a Latin root (we say anglicize, not *englishize) but in modern English there are also many words formed by attaching -ize to whole English words (the Oxford English Dictionary lists foreignize, jeopardize, womanize among others). I think this is what leads to variation in the spelling of words such as colorise/colourise and vaporise/vapourise. There's actually similar variation with the words crystallize/crystalize and metallize/metalize (where the Latin stems, seen in crystalline and metallic, had double ll, but the independent English nouns crystal and metal have single l).
Dictionaries rarely list vapourise/vapourize: it is not usual and is likely to be considered incorrect
Tristan r left the following useful comment referencing several British dictionaries that have entries for "vaporise":
the Cambridge English Dictionary says (UK usually vaporise). See
Longman English Dictionary says the same
I did not find any dictionaries indexed by OneLook Dictionary Search that have an entry for "vapourise", aside from Wiktionary, which calls it a "Misspelling of vaporise."
Based on this, I would guess that many British English writers would indeed consider it a misspelling.
The following question is also quite relevant: Should "glamourous" be considered incorrect?