Both are correct. The "sjuːt" pronunciation is more common in the UK, but the "j" (it's called a yod!) is very subtle. If you use this pronunciation, it follows you should use the other pronunciations which may stylistically adapt the "ju" sound instead of the "u" sound.

Speaking as a native British English speaker, the [sjut] pronunciation is old-fashioned to the point of being comical (I would say it if I was imitating an aristocrat or something). Modern English favours almost exclusively "soot".

There is an on-going sound change (Yod-dropping(yod-dropping is the elision of the sound [j])) by which /j/ as the final consonant in a cluster is being lost. In Received Pronunciation, words with /sj/ and /lj/ can usually be pronounced with or without this sound, e.g., [su?t] or [sju?t]. For some speakers of English, including some British speakers, the sound change is more advanced and so, for example, in General American /j/ is also not present after /n/, /l/, /s/, /z/, /?/, /t/ and /d/.