A reasonable amount just to cover the cost of the fuel would be �5.
Most employers who pay their employees if they use their own cars on company business pay them about 40p per mile for a car of the size you quote (making �10 for your journey). This amount is calculated to include fuel, insurance, servicing, wear and tear and depreciation. Most taxi firms charge about �1 per mile so, provided you don't ask the car to wait whilst you attend to your business, it should cost you �25 to �30.
Your sister-in-law is not justified in asking you to pay towards the upkeep of her car (apart from the fuel) for such a short trip. If it were me I would decline her kind offer and get a taxi, even if it meant paying a few pounds more.