It's not automatic that schools would pay for a CRB check, or indeed insist on one being done at all. I have to disagree that 'all schools do that for all adults in them', it just depends on how the adults are being used, what sort of contact they have with children and what sort of supervision the volunteers are under.
Many schools have parent helpers under very strict conditions, never leaving them alone with children for example. So a CRB check would not strictly be necessary.
I volunteer at both a school and a playgroup and neither would automatically CRB-check a casual volunteer. Again, of course, the volunteer would then be limited in what they were allowed to do and would never ever be left alone with children.
I would write or even better phone the places you are interested in, and just explain you want some experience of that sort of setting, with a view to doing the access to teaching course.
They wouldn't think you were mad at all, but may vary in how they react. Some will indeed 'bite your hand off', others will be a bit more wary of someone they don't know approaching them. But I should think it very likely you would get some interest.
Again, policies towards the CRB check will differ, and that is something you will have to broach with each school.