Watching news reports from South Korea it appears that we in the West are more concerned about the recent posturing by the North Korean leadership than South Koreans who would be first in the line of fire. As the US (and bit-part player the UK) ratchet up the rhetoric, perhaps the best strategy would be to just ignore the threats?
North Korea has a relatively new leader, who could be using this opportunity to buy valuable credits for future negotiations over aid. By talking up war, and then backing down at the inevitable talks to avert war, the North Korean leader can play the tough leader at home and the level-headed negotiator abroad.
Further, the relationship with China is not what it once was. North Korea can no longer rely on the silence of China, even less the support of China. This is not the 1980s or 1990s. China is increasingly looking to establish itself as a major rival to the hegemony of the US, and a noisy neighbour in North Korea will not help it fulfil its global objectives.
Finally, is North Korea really a threat to the US or the UK? I suppose the reality is that nobody really knows, but sensible analysis would land on the side of North Korea not being a threat. The country has been isolated for decades, increasingly so since the collapse of the USSR and the more recent cooling of relations with China. Despite a large army, North Korea would lack the capacity and might to conduct a modern war, especially against the US. It very much reminds me of the events that led to the invasion of Iraq ten years ago; we were constantly told that Iraq had WMDs and that it represent a real and immediate threat. We then watched US and UK forces invade with relative ease, against an Iraqi army that was inferior.
Every response from the US and UK will be met with more extreme threats and grandstanding from North Korea. In my view the best response would be to ignore the threats, and continue with quiet diplomacy about the wider issues of peace and poverty on the Korean peninsula.