Try and do more than one car boot, have a really good clear out, my dc are older so I sold some lovely children's books and because they were in good condition they sold for £1-2 each, which soon adds up. We had an old trike and two violins to sell as well as various odds and sods (cables, kitchen stuff, vases, toys for children to rummage through), made £180, which was very surprising. Paperbacks can sell well sometimes - I had a selection of Paulo Coelho books which sold quickly, maybe because they are not that common. If you have any seedlings to sell they can go down very well too. Children's clothes didn't sell well, neither did things like our travel cot (still have it) - so they might do better at nct sale, gumtree or on eBay. Any excess furniture, you could sand it down/give it a lick of paint, if you have any. Ask family and friends if they have stuff they want rid of, they might be quite happy to have a clear out. Make sure you take a flask of tea and food to the boot sale too.
We are having to be pretty frugal now, and we have started making our own pizza and bread (bbc good food website for very easy/quick recipes), we are amazed how simple, satisfying and much cheaper this is, we don't have/need a bread machine, the dc love it. We have less frequent trips to the shops bread is something I usually buy every couple of days (£1.85 for a large plain bakery loaf, pizza 2 for £5+ once a week). Being at the shops less really cuts my spending! Dh takes lunch to work and his own coffee, he also started commuting by train, which has saved on petrol.
We have a very knackered car, older than yours, it would probably not be worth repairing but like you it is too expensive to contemplate trying to replace it.
MSE website worth a look to make sure you are getting the best deals on energy suppliers etc.
If you live in Scotland you could look into wild camping - free and legal, but obviously it means you have to enjoy really roughing it! You can shower at a local pool?
I know being skint is rubbish, but as long as you are not starving, keep an eye on your long term goal of studying, if you can do the studying sooner rather than later go for it. My dc both bf'd until 14 months but by that age they only tended to bf morning and evening, or maybe a little more if they were ill, so I wouldn't let it be a barrier to your education. Good luck.