If you have enough money from work, Travelodge are safe and some are very cheap, depending on what area of the country you're in.
I've stayed at Youth Hostel Association places for about £10-£15 a night. I know of a place in Manchester
It is here www.yha.org.uk/hostel/yha-manchester
in case you're in that area. Some nights it's only £12.
I kno it may not help now, but in the future make it an absolute priority to build up an emergency fund. Even if it means going without coffees, chocolate bars, little treats - just try to put even £10 a week aside into a separate account and build it up week by week. Even having a hundred pounds can make a world of difference to your options if anything happens again.
I'd echo the other people who've said wait a few hours somewhere warm if you can then phone your mum.
BUT, one thing I do want to say is we don't know the poster's situation. We don't know if her mum and boyfriend, and her bf, are nice people. There are no guarantees.
Can you tell us which city or county you're in?
If you do stay in your car, please be careful.
Have you considered being a lodger? I found a place that was £350 all bills included apart from any phone calls I made from the landline. It was a lovely house, massive, really nice garden, with a deputy head teacher. It was safe.
Or maybe a studio flat if you can afford that on your wages? Obviously bills included makes life a lot easier.
I'm sorry you're in this situation.
If you decide to stay in your car, please google about where is safe to stay. Do you have a car charger for your phone? You can buy them at garages.