I agree with Jack's analysis of the UK statement.
I would add that the British legal position is not new. The British relied on the doctrine of humanitarian intervention for their participation in the NATO bombings of Kosovo in 1999 (when the Clinton Administration asserted no legal basis) and to police the No Fly Zones in Iraq during the 1990s (while the Clinton Administration relied on the pre-existing UNSCRs 678, 687, and 688). The three conditions set out in the new British statement are virtually identical to the conditions articulated by the British Government in 1999. The criteria were quoted and discussed in an article by Sir Adam Roberts (now President of the British Academy) in an article in Survival in 1999.
In contrast, as I noted in my op-ed earlier this year in the Washington Post entitled "U.N. Rules and Syrian Intervention," the US Government, under both Democratic and Republican Administrations, has been reluctant to recognize a legal right of humanitarian intervention lest it be abused by countries with less laudable motives.
For a thoughtful discussion of the past and present positions of the British government on humanitarian intervention, see this article in yesterday's Guardian, quoting former FCO Legal Adviser Sir Daniel Bethlehem as saying that, depending on the facts, self-defense and humanitarian intervention are both "credible legal bases that may possibly be relied upon in justification of a use of military force … in response to the use of chemical weapons by the Assad regime against the Syrian civilian population."