Hi Kate,
For the company car user, you can reclaim the VAT element (i.e. 1/6th) of the 11p per mile. You can also reclaim VAT on the business use by the private car owner – but not on the full 45p, as this amount is also intended to include a contribution towards non-fuel costs. In theory you can use any recognised published fuel rates to count as the “fuel element” of the 45p. But unless the amounts involved are huge, it’s probably easiest to use the same HMRC Advisory Fuel Rates that you’re already using for company car users.
In both cases (company car and private car users) the employee should obtain VAT receipts when they buy fuel and submit to you with their claims – which you’ll then need to keep on file. Clearly the amounts on the receipts won’t tie up exactly to the claim values – but in total there should be sufficient receipts submitted to cover the 11p per mile being claimed.
HMRC guidance is in sections 8.8 – 8.10 of HMRC manual 700/64: https://www.gov.uk/guidance/vat-on-motoring-expenses-notice-70064