I would use four in careful speech. (For me, at least) it is machine + -ery, not -ry. That said, the schwa (weak vowel represented by <e> in this word) is liable to disappear between two such consonants as [n] and [r]. It could easily be three syllables in normal speech.
I can't say anything about the accents in England. In the States however, I have heard the word pronounced as (MA-SHEEN-RY) Don't ask me which state the person was from because I don't remember. I also didn't make any assumptions about the persons education because some Americans have a bad habit of doing just with nothing other than a persons accent as the only determining factor.
It really depends on the word. For instance, you'll probably find a vast majority of people pronoucing chocolate as two syllables. Conversely, policeman is more often a three-syllable than a two-syllable word.
(from what I've heard, that is).
I was once in a phonology class where we tested our own pronunciations of such words. I couldn't see any logic to what I said. There are some words - among them temperature, general, different - where I cannot use a schwa even in careful speech: it just strikes me as a mispronunciation to add the extra syllable. There are many others where there is an underlying schwa, deletable by a normal phonetic process depending on speech style.