You can claim back the VAT provided the person selling the van is VAT-registered
Doesn't matter if the vehicle is new or second-hand although if new (ie from garage) then you can be virtually 100% sure that the seller will be VAT registered and so VAT will be charged and therefore will be reclaimable.
You can then get capital allowances on the full (net of VAT) cost of the vehicle. Basically this means you get to write-off the cost of the vehicle in 8 equal instalments over an 8-year period.
HOWEVER if you purchase the vehicle via Finance Lease then you DON'T get capital allowances but can write off the actual finance lease repayments as you incur the cost of them.
You will pay BIK on the vehicle but the amount will be very small, generally speaking