Alright, quiet in the cheap seats!
Problem solved.
SWMBO's Uncle who lives not far from us gave me a jump start and it started effortlessly first turn of the engine. In fact while I was waiting for him to arrive I tried the headlights on high beam and they seemed to be fine without any dimming of the dashboard lights, so I suspect with the rise in temperature from -6 to 1 degree that the battery may have actually started the car without a jump start, although I didn't try it.
I then drove to Halfords for the new battery. After getting there I tried starting it on the old one and it did start ok - but bear in mind not only had it had 15 minutes of charging by then, the heat in the engine bay will have warmed the battery up to 20 degrees or so, making life much easier for it. Starting again in sub zero conditions would be a different story.
With the new battery it's turning over quite obviously quicker than it ever has since I've had the car, let alone during the recent cold weather.
The real test will be the next really cold morning of course. Tomorrow is forecast to be "only" -3 degrees but we will see how it does there given that it hasn't had a lot of charging.
Interesting that whilst the outer flange mounting dimensions and post locations of the new and old battery match, the old one is a bit lower and smaller in girth around the middle with the new one looking quite a bit more beefy. Visually at least the new battery looks to be of quite good quality.
I did a voltage measurement after the car had been running for 5 minutes and it was 14.0 volts. With the headlights on dip, fan on medium and rear window demister on I was still seeing about 13.8v - I think that's about par for the course, especially if the new battery isn't fully charged.
Thanks everyone for the advice that let me get this sorted out pronto!