Firstly, don't let this affect your A-Level exams, as the above poster said, you can always defer a year to take some time out and save up a bit of money then re-apply again next year instead if you think the money is going to be too much of a problem. Your A-Level grades are more important than anything else right now.
Otherwise, I would start by looking for jobs over the summer as soon as you can to save up as much money as possible before the beginning of the course. You've potentially got 3-4 months where you could be working full-time and giving yourself a very comfortable buffer to live on. Try the temping agencies (e.g. Blue Arrow) if you can, and get in there early because temp agencies get loads of students over the summer so get to the front of the queue for those jobs now rather than later.
Also, how have you calculated the £19 per week? I don't know what the timetable of your course looks like, but most typical degrees only involve living at university around 28-30 weeks per-year, then living at home for the rest (Easter, Summer, Christmas). Obviously those holidays are good opportunities to get earn more as well.
In terms of making the best use of your money at university, it's mostly going to be about being smart about what you buy - especially when it comes to food.
A few ideas:
- Most importantly, learn to cook for yourself using good cheap staple ingredients. Avoid convenience foods because those are always hugely overpriced.
- Look for local markets and independent shops to buy food, because those can often be much cheaper than big shops.
- Wherever possible (long lasting cupboard food, household stuff, etc) try to buy it in bulk when it's on special offer for half-price or buy-1-get-1-free type deals.
- Go out of your way to find Discount stores like Aldi/Lidl and any local/independent discount markets. Also remember that you pay for convenience. So if a shop is in a convenient location (e.g. city centre tesco express) then the prices will be much higher than the Aldi or Lidl in the middle of nowhere out of town.
- Get to know the closing times of food shops and make a habit of getting there around 20-30 minutes before their closing time because that's when they'll have lots of heavily-reduced fresh food which goes out-of-date that day, but will usually still keep for a day or two longer, and you can always freeze it -- especially if the shop has a fresh bakery too. Even in super-expensive shops like a city-centre M&S food hall you could find a fresh loaf of bakery bread down to about 10p when it's within minutes of being thrown away, so timing is everything.
Also try to find out what the kitchen facilities are like at halls - do you need to bring your own kitchenware to cook with? Make sure you take a few tupperware boxes with you to Uni so that you can use them to freeze things. A microwavable dish would be a good idea too.
Do some research into the cheapest way to travel - e.g. can you buy a student bus pass which lasts the whole year?
What about the cost of your phone? can you save anything by getting a cheaper contract or switching to PAYG if you haven't already?
When it comes to items like clothing, can you get by the rest of the year with everything you have now? Probably safe to assume you won't be making any purchases like that at uni. If you do need to spend money on anything then always do the research beforehand. high-street shop prices and prices you see on the first page of Google results are usually the highest from bigger companies who spend more money on marketing. It takes time and effort to find cheaper options, discounts, second-hand items, etc..
Have you got everything you need in terms of computer equipment already? Does your university have facilities and provide you with student licences for things like MS office so that you can work at home? Best to get that sorted over the summer if not. (If your university won't give you an office licence then you can buy Office 2016 from any reputable ebay seller for about £3)
If you need any books for the course, you will probably be able to get by just with the Uni library - but if there's any you need that you can't get at the library, see whether any 3rd year students have any they'd like to sell or give away.
However, unless you're going to be earning a decent amount of money over the summer to live on, and at least some money during the term time, you're not going to have any kind of social life at uni, so I would think really carefully before attempting to live on £19 a week. It's not impossible but it could be pretty miserable. The way things are right now you won't even be able to afford to buy a coffee from the student union bar.