Interior lights and car locks not working properly

After a really frosty weekend, when I drive, the front and back interior lights come on and off. If I turn it on at the front while driving, then turn it straight off, it stops, until I slow down to a stop, then it begins again. I then noticed the car wouldn’t lock. I press the fob button, and it makes a ‘double’ clicking noise, but doesn’t lock. I can lock the drivers door with the key after about 4 attempts, but this is the only door locked.
In the past, I have had trouble closing the boot on really frosty mornings, but I’ve not noticed that problem over the last year.