"Fill it up" or "Fill 'er up" in BrE too when at a serviced petrol station (few and far between). When at a self-service petrol station, we would just say to someone "I'm going to fill up with petrol" or "I need to get petrol". Needless to say, we don't always put a full tank of petrol in the car. The price of petrol in the UK prohibits that for many people!