0 abbreviation for Her Majesty's Government: the UK government:
We are disappointed that HMG has felt unable to support the reform.
1 abbreviation for Her (or His) Majesty's Government: the government of the UK, which has the Queen (or King) as its head in name, although she (or he) has no actual political power:
We support a renewal of the treaty, an objective which we know is shared by HMG.
If a minister had done something really bad I don't think HMG would be prepared to go out on a limb to support him.
HMG's official position is that we do not negotiate with terrorists.
I am a representative of Her Majesty's Government, and my priority is serving HMG.