The ideal job would be flexible (you can pick and choose how much work you do, and can disappear for a month before exams without a problem), has a high hourly rate of pay (so you've more time to spend studying for the same amount of money), has little to no commuting time (eg, based where your medical school/uni is, or involves working on a laptop at home or in the library), is reasonably low stress, and has relevance to your medical studies.
Shifts at Asda would only hit a couple of those boxes (maybe commute, maybe low stress?). Ideally, you'd be looking to tick off three or four at least, if not all.
Unfortunately most of the 'ideal' jobs involve leveraging existing skills, qualifications, experience, and contacts, and therefore by definition are rarely available to school leavers. Most of the success stories I've heard of have been qualified nurses, HCAs, and pharmacists working bank shifts, or (as I'm hoping will be in my case for next year!) professionals freelancing for their old employer or other clients, for example consultancy, editing/proofreading, web design, and so on. If you can develop any skills or experiences in that direction, it's definitely a bonus.
Tutoring is quite fun, particularly if you pick it up in later years (this is what I did during my first degree). However, it is a logistical challenge, it can be quite emotionally draining, and it's actually quite a commitment - you can't just abandon a poor A-level/Highers student a few weeks before their mocks because you're getting stressed out. But on the plus side, once you build up a few students, you can re-use a lot of the same learning materials, and it's fantastic experience to have both for the CV and your teaching skills generally. If you're around in the summer, tutoring first-years who are doing their resits is a good call, as you won't have other stuff on.
One thing I'd recommend is to have a read of Merys Jones' blog, in which she details the day-to-day grind of working two jobs while studying medicine. It's a hard read, but an important one if you're considering this path:
http://bloodystudents.blogspot.co.uk/