An executor is generally only allowed to reclaim out of pocket expenses.
Generally speaking, executors are family members or close friends of the deceased, and as such would only claim out of pocket costs such as legal fees. It can leave a very sour taste amongst beneficiaries if the executor is claiming for mileage. Being chosen to act as an executor should be considered an honour and a privilege. The position should not be abused, particularly if you are one of the beneficiaries.
Sometimes the will nominates a professional person (e.g. solicitor or accountant) to act as the executor with the stipulation that the executor may charge a professional fee. In such cases a mileage rate of, say, 40 cent a km would be considered reasonable.
In your case, you are of course entitled to claim mileage if the mileage was incurred wholly exclusively and necessarily for the purposes of carrying out your duties. However, you should consider how your claim will be perceived by the beneficiaries. etc.
Jim Stafford