As you are VAT registered here you should provide the UK business that you are buying the van off with your VAT number. They will proably ask for some headed paper also. They will invoice you at 0% UK VAT.
You should self-account for the Irish VAT arising in the period you purchase the van. Basically this means that you increase your sales VAT by cost*13.5%. Assuming that you have full VAT recovery you also claim a deduction in the same period of the same amount, so there is no VAT cost, more of an admin thing.
Hope that makes sense!