In his CPD (1972) Jack transcribes this word as ɡʌvm̩ənt, and entirely iɡnores the possibility of n before the m. See also his comments in §10 of this review.
the term government … can be heard every day over and over again in countless news bulletins and current affairs programmes. Both EPD15 and LPD list first the variant which contains the /-nm-/ sequence. However, anyone who listens at all attentively to recordings will soon discover that this is not merely not the predominantly heard form of the word, even in situations of the greatest prominence or highlighting, but that it is actually even a relatively unusual form of it.
Now Giovanbattista Fichera writes to take me to task over the same issue, expressing surprise that I have not acted on Jack’s criticism. (In LPD the main entry (BrE) for this word continues to read ˈɡʌv ən mənt.) GF continues
In my opinion, it requires a great deal of effort to articulate the <-nm-> sequence without assimilating the n to the m. In Italian, San Mauro is sa'm:auro not san'mauro. It seems to me that mm is not a variant/change in progress, but the rule.
I think my entry is correct. It unquestionably corresponds to my own slow-careful pronunciation of the word. I certainly don't have to make “a great deal of effort” to pronounce it as shown. (But then my L1 is English, not Italian or Japanese.) The alternatives that follow represent reductions which are also admittedly very common in speech - but they are just that, reductions.
I am in no doubt that for me (at least) ˈɡʌvənmənt accurately represents the succession of articulatory targets presumably stored in my mental lexicon as the phonological specification of this word. As I told GF, it also represents the way I pronounce it when articulating carefully (not overarticulating, but also not applying running-speech reductions).
Some of these reductions may indeed be frequently heard from speakers, in radio or TV news bulletins as elsewhere. That does not make them the mentally stored forms, which are what I think a dictionary ought primarily to record.
As for GF’s comments on San Mauro, he is perfectly correct as far as Italian is concerned. Italian, like Spanish, Japanese and various other languages, does not admit sequences of nasals at different places of articulation. But English does. Even JWL’s CPD shows -nm- at inmate, with no other variant given. (In LPD, on the other hand, I do recognize the possibility of ˈɪmmeɪt, derived automatically by applying the option of dealveolar assimilation.)