Charities are covered by normal VAT rules, but VAT only applies to 'business income'. Most charities have some business income to raise funds but they only have to register if this income is over the threshold. Donations are outside the scope of VAT and don't count towards income threshold.
I had this problem with a charity I was doing the books for too.
They had 95% of their income from donations but also sold some vatable merchandise.
They thought they could claim all the input vat for all their activities ie exps for events. But the vat office said they couldn't claim the portion of the input vat the resulted in the donation income - ie 95% of the input vat. So they de registered.
Ah. I knew it wouldn't be starightforward. TBH, it's probably going to be more hassle than it's worth then. I'll have to bite the bullet and ring HMRC. I can never get a straight answer from them normally.
In general, the normal laws of VAT cover charities so they do need to register if they have VATable trading activities which are over the threshold. To avoid the complication and inefficiencies of partial exemption, it is common for charities in this situation to put these activities into a trading subsidiary. This would need to be set up professionally, although I believe the Charities Commission may give some free guidance.
In general, childcare is exempt from VAT.
Education is not zero rated, it is standard rated unless it is provided by an eligible school or college or qualifies as private tuition, in which case it is exempt.
Unless you are providing zero rated services, it is hardly ever worth registering unless you have to, but if there is any doubt you should seek professional advice. With respect, I would not normally expect advice on VAT efficient structures to be within the scope of bookkeeping services: apart from anything else bookkeeping PII would not cover it and could leave you personally liable.