Hello Robert, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
You are correct in your surmise as to the the input tax reclaimable on purchase or lease hire providing there is no private use of this vehicle. Fuel costs input tax may be reclaimed as normal. However, you would have to be registered for UK VAT in order to achieve these reclaims.
I do hope that you have found my reply of assistance.