I did it at Barclays at the end of year 10 instead of 11. I started off asking lots and lots of banks (Santanders, HSBC, Lloyds, Barclays, Natwest). I phoned and emailed since they all said they offered it, but most didn't reply.
For HSBC, search for work experience for 14-16 year olds and it will come up somewhere on their graduates website. I think there's an online form you fill out after signing up which you have a deadline for January probably. They will email you back in your account with interview times, you choose the interview time, most are during school hours - in the mornings at 9, so tell your school you'll be there instead. They'll ask you 3 questions and you just answer, they email you back. I did fine but one question I kinda failed.
For Barclays, go to their LifeSkills website, sign up and complete all the tasks they tell you. They tell you to do little quizzes about stuff like money, skills, personality. You can have more than 1 go I think. Anyways, the max you can get are 1000 points, for work experience, you need 200 I think. After you've got it, print out the certificate that you get (to show you've got the points and are eligible for work experience). Then, go to the teacher in charge of Work Experience at your school, show them your certificate and tell them that they need to go on LifeSkills and probably sign up as a teacher and fill you in for Work experience because you won't be able to do it yourself. Hopefully, they will sign up and email the branch and you'll get it
Edit: I just saw your other post, where I did it, there were two branches, one main one where there were PB's, cashiers, meetings etc. The other one was 2 minutes away and had 2 cashiers and that was it, automatically, when your teacher emails the branch, it'll go to the main one probably.