Dodgy start up

Check the connections to the battery, the block and the starter. It's likely some or all of them are corroded. Not just the terminals on the battery posts. Check the terminals on the starter as well. Examine the jacket on the leads and if they're showing signs of cracking or corroding inside consider replacing them. It's not uncommon for a car this old to have trouble with these wires.

HOw cold?

Good advice from Bill. In addition to the red battery+starter cables, check the ground/earth strap (usually a silver colored braided thing that ties the engine and/or tranny to the body).

I don't know how they do it in the UK, but on this side of the pond you can go to your local auto parts chain store and they'll check the CCA or Cold Cranking Amps of your battery for free. CCA is a good indication of your battery's health.

Not that cold, about 12 degrees of frost. Thank you for contributing. Tony

Not hat cold? Yeesh, you've got a much high tolerance than most.

That's cold enough to be looking at metal contracting enough to open gaps in corroded connections. A loose battery terminal or other bolt point that's got corrosion accumulated in it would certainly contract in the cold. Allowing more corrosion to develop in the process. Loosen up the cables, clean the connection THOROUGHLY and reattach. You should generally do this anyway every 5 years or so. It's entirely possible your battery is dying as well. But clean the cabling first and replace any that look like they've got corrosion going up into their strands. These wires are cheap from a parts shop so it's not like you'd going to break the bank. Then biggest hassle will be doing it in that 12 degree weather! Brrrrr!