Im not sure about charity shops, but theres no harm in asking if you can volunteer there at 15.
How about volunteering at your local rainbow/brownie/guides group. You can volunteer there from 14.
Good on you for wanting to volunteer. I agree with Emma above :-)
I volunteered at OXFAM aged 15 - I just wasn't allowed to work on the till on my own, but I could do everything else.
If you want to volunteer for a specific charity it is worth looking at their website for details; you could also ask at school if there are teachers who run the Duke of Edinburgh award, as even if you're too young to do it now, they may be able to set you up with whatever charity they use for the volunteering section of it.
Oxfam, british heart foundation and save the children will all let you volunteer under 16 in their shops. I believe others will too.
I think charity shops might let you help put out or arrange the stock, even if they won't let you work the tills. Volunteering with Rainbows/Brownies/Guides is very fulfilling also. I have been volunteering with my local Brownie pack for some time now and it's surprisingly enjoyable! I'm sure most places will be pretty accommodating if you ask though!
Libraries are good places to find volunteering work and they usually need a few extra helping hands - plus they allowed me to work behind the counter and I was 14.
Charity shops will probably let you do everything apart from using the tills until you're 16. Good on you for wanting to volunteer! I worked in a charity shop after I left uni until I started my job and it stopped me from going crazy!!!