Just my opinion but you will be better off buying a block of lessons for £15/lesson than buying a car before hand. Usually you can pass within a block of 10 lessons and then its much easier to sort out insurance ect.
That's still my feeling too, especially given that you don't have a licensed driver with you now. It sounds like a tonne of worry and concern where it doesn't need to be at a much larger expense. Once you have the full license, then you can look at if you want to buy a car. You'll be far better off having your practice with someone who can help you fix bad habits and get you used to having someone watching so your nerves don't get the better of you when you have the actual exam. Most people here learn that way.
Not to mention that your driving abilities may have little relation to the timeframe of when you can pass. I started my process of getting my license around this same time of year and it was about February before I was able to get it, and I passed on my first test. I didn't procrastinate anything--every step of the way took much longer than I thought it would. Even the theory exam took forever to book as the testing centre was full. Then when I scheduled exams, they kept moving my dates back due to an examiner that was on sick leave.
I pushed hard, completely convinced I'd have no trouble finishing before the end of the year, and I nearly lost my job because I didn't have a license after November. It was a nightmare. If you are renting parking space and paying for car expenses and insurance, it could add up quickly if you end up taking longer than you plan and have a car you can't use. I just really think you'd be wise to wait on buying a car. They are more expensive than the purchase itself--car, road tax, insurance, petrol, maintenance, repairs, parking fees, congestion charges, etc all add up fast. Or you can do as the last person suggested and just buy a group of lessons and practice for a lot less with someone who will better prepare you. You'll need the lessons anyway as knowing how to drive and knowing how to take the test are two different things.
As to buying a car . . .
One thing you can do when it comes time to buy a car is ask around with people to find a reputable garage. It's more hassle, but my mechanic has a service where he'll give cars a run-over before you buy them to see if there are any obvious problems that have been hidden from you. You can do that before buying, if you are worried--then there is more peace of mind.
If just going on your own, pay attention to how it sounds, is it sputtery? Is it smooth? how tight is the clutch pedal--replacing a clutch can be very expensive. Is the MOT pretty new? Don't get one that doesn't have most of the year on it's MOT--they could be hiding something and then you end up paying more than the car is worth to repair it or buying a new one with clean MOT. Also, don't rely on the MOT as a bill of health. Don't stress about it though. I bought my first UK car on my own where my dad had always helped before. It was scary, but I got him to knock £140 off the price! It was a little junker too, but served me well for a couple years before it failed MOT and was too expensive to fix. I just looked at it as having got my money's worth out of a cheap car, then I sold it to one of those buy any car websites for £120. Of course there were lots of other expenses in-between, but it worked out okay.