You don't need a CV for many hospitality and retail positions. In my experience, small shops and cafes are the best for hiring young staff: usually you'll see adverts for 'Part-time wait staff,' or 'Saturday assistant,' in quite a few windows in your local town. After you find an advert, simply go in and ask to see the person in charge of hiring staff (Top tip: Never inquire about a hospitality job during service hours) -- he or she will most likely chat with you a bit and judge your personality for the role, and likely ask a few questions about why you'd be good for the job. More often than not, if you are a confident and out-going person, you'll acquire a trial shift where you will prove your capability.
If you are ever asked for a 'CV,' you aren't expected to produce something professional, simply your contact details and a few examples of your personal skill set. If for example, you were applying to a coffee shop, I would recommend simply writing a couple of paragraphs about how you appreciate communicating with people, and that you aficionado of good coffee. In any case, you definitely need some piece of paper with your phone no./email on.
Personally, I'd steer away from big corporations. There is a huge amount of bureaucracy, and since it's normally the case that the staff impose an unwritten hierarchy, you'll get the crap shifts and the few hours, while the veterans will get long shifts on good days. Also, they tend to pay as little as legally possible for your age (£4.20), whereas small businesses will (frequently) pay the NLW of £7.80 -- although employers vary hugely of course.
Source: I worked since 15 in six different retail/hospitality positions over the course of seven years.