Is it permissible for an engineer to take the taxi fare provided by the company if he uses his private car to carry out company work, knowing that taxis are not always available at the work site?

You are not permitted to use your car for work errands unless authorized by someone empowered to grant such permission. This is because the company's policy dictates the payment of actual costs for assigned errands. And according to the sound (juridical) opinion, an agent cannot lease from himself to his principal unless he is granted permission to do so. However, if the company permits you to use your private car for work errands and to receive the customary remuneration for that, then there is no harm upon you in that instance.