VAT becomes applicable if a supply is made for a consideration. If a person is participating/speaking at an event then this would normally construed aa a supply and the 'consideration' would be the payment they receive.
If the speaker is overseas then this would come under the general rule of services, which would mean that as long as you are a business, then no VAT would be charged and the supply would be subject to the reverse charge procedure.
Place of supply of services (VAT Notice 741A)
If the speaker is in the UK and is VAT registered then normally VAT would apply.
However we would recommend contacting our charities team for further advice, as there are special reliefs for charities in relation to VAT.