What relief can be claimed for journeys using another person's car?

My girlfriend recently started occasional temporary at a location that isn't her permanent workplace and is 80 miles from her permanent home. She doesn't drive, so we use my car for me to drive her to and from her permanent home and the temporary workplace. We don't live close to each other, so I also drive to and from her home (also 80 miles each way) to pick up and drop off for those journeys. I incur the initial expense of fuel and running costs, on the understanding that they will be repaid by her. I don't keep receipts for fuel purchases (which includes my private use), but I do keep a mileage log for these journeys. She is not paid any travel expenses by the employer. In this situation, what relief is available; how should it be claimed; and what documentation/information must be recorded or provided? The guidance (https://www.gov.uk/tax-relief-for-employees/vehicles-you-use-for-work) says that reliefs are available when "Using your own vehicle for work", but doesn't say anything about relief for travel expenses incurred using vehicles owned and driven by someone else (e.g. a partner or friend) and who also incurs the initial fuel and running costs. From what I can see, EIM31800 and EIM31200 don't provide any information about this type of scenario.

Hi

Normal commuting to work is not an allowable expense.
To get relief for the cost of travel, the employee’s attendance at the temporary workplace has to be necessary in the sense that it’s dictated by the requirements of the duties of the employment and not, in any way, by the personal convenience of the employee.
For temporary workplace, please refer to EIM32075 - Travel expenses: travel for necessary attendance: definitions: temporary workplace
If applicable and expenses are due, it would only be the passenger rate that would apply as she is not the owener or the driver of the car. You also cannot claim for the mileage to pick her up.

Thank you

Hi, Thank you for the reply. Regarding the 'passenger rate' which you say would only apply (if applicable), my understanding from the GOV.UK guidance (https://www.gov.uk/expenses-and-benefits-business-travel-mileage/passenger-payments) is that it is available to employees using their own cars and carrying fellow employees as passengers - which does not apply in our situation, so I am unclear about how it could be claimed for. Can you share a link to the relevant guidance that confirms/describes the basis where the passenger rate would apply in our situation? Thank you.

Hi James,
The Income Tax (Earnings and Pensions) Act 2003 (ITEPA) states that in order for a travel expense to be allowable, it must satisfy one of two tests:
It is “necessarily incurred in the performance of duties” (ITEPA s.337)
The travel is “for necessary attendance” (ITEPA s.338) 
Additionally, the employee must be “obliged to incur and pay them as the holder of employment” (ITEPA s.337(1)(a) and 338(1)(a)).                                                                                    as The car is not hers and she is not paying for travel then no mileage is due"
Thank you.