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The best school I've been to wasn't BHS approved. Something to do with not individually stabling their horses apparently. My child attended when she could. Ponies and instructors make schools. Not necessarily facilities.
I wouldn't necessarily avoid if not BHS approved, but I'd really take my time looking at the standard of horses and their care, the standard of teaching etc. (and their insurance and safety practices) But if I wasn't horsey myself and was looking for lessons for a beginner I'd probably go for BHS approved or similar to be sure of basic standards