Is [bʊt] (Northern England) analyzed as an allophone of /bʌt/?

In some/most Northern England accents, words that have [ʌ] in RP (or standard varieties of English) are pronounced with [ʊ]. So hut, cut, shut etc are pronounced with [ʌ]* in Southern British English but with [ʊ]** in Northern English accents.

Are Northern accent classified as separate accents and have been assigned a separate phonemic inventory or are they analyzed as a dialect of the Southern English accent and those pronunciations are analyzed as allophones of the pronunciations in Southern English?

In short, is [bʊt] of Northern English analyzed as an allophone of /bʌt/ or does Northern English have its separate phonology and analyzed as /bʊt/?

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… * and **: I’m not sure about the exact vowel quality but to avoid confusion between "phonemic" and "phonetic" transcriptions, I use square brackets.