I remember this well (around the same time the US produced a similar drama called 'The Day After'). Scary stuff.
A thing I'll never forget is that at the time I was a young lad working in Croydon, and a few weeks after these were both aired, the sirens went off. Not just the continuous 'all clear' but the full on rising and falling alert. Being at the time of the Cold War, this was absolutely terrifying. Cars on the Croydon flyover were slowing down/stopping and the drivers were leaning out of their windows. The sirens continued for a couple of minutes before stopping.
I heard later that it was something to do with the testing of the sirens in case of the Thames flooding, but it was bloody scary at the time, and talk about bad timing!