The offglide of the English diphthongs /aʊ/ and /əʊ/ is represented by the vowel /ʊ/. In other languages, such as Portuguese and Spanish, they are represented in the same way, but they sound completely different. The offglides in British English are definitely more fronted. Do you think [aʉ̯] and [əʉ̯] could be more accurate representations? In Portuguese (my native language), the tongue slides back towards /ʊ/ (or /u/) in those diphthongs, but it seems that that doesn't happen in English. What are your thoughts about this?
The backness of the final element of /aʊ/ and /əʊ/ in British English varies between different accents/speakers. (For the MOUTH vowel, an alternative realization used in in some dialects is a long monophthongal vowel that lacks any kind of offglide, possibly something like [aː]).
The transcriptions [aʉ̯] and [əʉ̯] are reasonable, but whether or not they are "more accurate" depends greatly on the specific pronunciation that you are trying to transcribe. The IPA symbol ʊ already implies a quality that is not completely back; a distinction in quality from Spanish <au>, as in raudo, could be marked by transcribing Spanish with [au] or [aw] (and in fact, I think I've seen those transcriptions used more often than [aʊ] in the context of Spanish).
I'm not sure about the situation in Portuguese; it may be the case that for this language, the symbol [ʊ] is used instead of [u] only to mark that the vowel is not entirely close. That is, perhaps Portuguese [ʊ] could be more accurately transcribed as [u̞] or [o̝].
Welcome to the chaotic world of IPA vowels!
Sadly, the IPA vowel chart is kind of lacking in the vowel department, which makes answering this question difficult. The space of vowels is completely continuous, unlike e.g. the space of plosives, and the IPA vowel symbols aren't anchored to any particular phonetic feature that we can measure:
[i], for example, is "the highest, frontest vowel you can make", but a Bantu
[i] is generally significantly higher than an English one.
In my own experience, the English "W-esque" offglide is somewhat more centered than the ones you'll find in Romance, both less back and less high (and often less rounded). But for a proper comparison, you'd want to get recordings of both English and Portuguese diphthongs, then run formant analysis on them.
Formant analysis is a wonderful technique that revolutionized phonetics when it was discovered. Essentially, it can show us exactly how high and front a vowel is, with objective, reproducible numbers. (It can also tell us sort of how round or nasalized a vowel is…those aspects are harder and less precise, unfortunately.) So by comparing the formants of English and Portuguese off-glides, you can say precisely how high and back they are, then compare those numbers.
(Someone may already have done this—but if so, I wasn't able to find the data online. If you know where to find it, please feel free to comment or post a new answer!)