The following correction was printed in the Guardian's Corrections and clarifications column, Saturday 8 May 2010

In this piece we wrote: "BP says you get around 28 miles extra from a tank of super-unleaded petrol." In fact, BP says you can get "up to" 28 miles extra. On average, it says, the actual extra is about 13 miles per tank.

I don't hammer down motorways. I don't break speed limits. I've never been responsible for a car accident, and never had any points on my licence. I think of myself as a cautious, weekend-only driver (I cycle weekdays) who chugs along in a 10-year-old estate car. And like everyone else, I'm horrified that filling up my tank sets me back more than £70. So when BP invited me to spend a day learning how to drive all over again, lose my bad habits and gain some good ones, I was sceptical. Would it really make that much difference to my petrol consumption?

The answer is: yes. My first test run was in a diesel-engined Mini Cooper, and I clocked up what I thought was a respectable 39.6 miles per gallon (mpg). Yet automotive engineer Anthony Sale drove the same Mini round the same track – at Millbrook Proving Ground in Bedfordshire – completed the course faster than me, and achieved an extraordinary 63.3mpg. In other words, I can get 60% better consumption, produce lower emissions and still drive faster. What's the secret?

Millbrook is familiar to viewers of the BBC's Top Gear: a vast high-speed bowl for extreme vehicle testing, a five-lane motorway, hill routes and mock city streets, all security-patrolled as car manufacturers put top-secret models through their paces. And, last week, there was me, pootling around, an Aston Martin often on my tail, and superbikes scorching past.

But back at Millbrook mission control, the computers linked to the Mini's engine told a different story. I wasn't pootling. I was over-revving, driving in too low a gear, accelerating and decelerating too much, and failing to react properly to road conditions.

The computer spat out its conclusion: I am a rubbish driver, I'm wasting vast amounts of money on petrol and destroying the environment. If I drove efficiently, I could save £7,734 over 10 years, and cut 16 tonnes of CO 2 emissions. OK, that's if I were driving 15,000 miles a year at an average cost of 119.9p a litre, whereas I drive around 4,000 miles a year, so my savings would be lower. But I can see the point.

So what am I – and millions of other drivers – doing wrong?

Over-revving

I never look at the rev counter – but Sale tells me I'm letting the rev count go too high before I change gear. He says I'm not alone – drivers typically let the revs run to 3,000 per minute on a petrol car and 2,500 on a diesel before moving up a gear; Sale says we should be changing up when we hit 2,500 revs on a petrol and 2,000 on a diesel, and move into fifth (and sixth on new models) at the appropriate point. I listen to the engine before moving up gear – so I've got to change my listening habits. And going into too high a gear too soon is also wrong: "Labouring the engine in too high a gear can actually increase fuel consumption," says Sale.

Acceleration and deceleration

"Stamping on the brakes and then accelerating hard is efficient driving's worst enemy. An efficient driver is a smooth driver," says Sale. The computer shows that I accelerate too fast out of roundabouts, and decelerate to a halt at junctions. On the motorway stretch, I go up and down between 60mph and 70mph when it is crucial to maintain a steady cruising speed.

By contrast, the graph of Sale's driving shows that on sections of the track he is not using any fuel at all. This is when he's cruising in gear towards a roundabout, letting the car slow by itself. I, on the other hand, occasionally put the car into neutral and let it coast, which is a no-no. "Lifting off the throttle, rather than putting it in neutral, means you will use no fuel at all," says Sale. It's safer, too.

Speed bumps

Braking hard, accelerating, then braking hard for the next speed bump means your car will drink petrol, says Sale. He tells me I should instead drive along speed-humped roads at a steady 15-20mph.

Speed

Saving fuel is not just about driving more slowly. Sale is relaxed about whether I drive at 55mph or 65mph. The real cost comes at above 75mph. Your engine may not sound like it's labouring, but in reality it's when your engine starts glugging on the gas. "At very high speeds engines will rev higher and will no longer be in the economical 2,000 to 2,500 rpm band. At this point the engine will have to work much harder and start to drink far more petrol," says Sale.

Will I now change? Yes and no. The next day I was driving the mean streets of south London. Instinctively, I accelerate to get into the right lane, I dart away when lights change, and I frequently slam on the brakes at an unexpected speed bump. But I have started to look at the rev counter, listen to the engine in a new way, and slow down differently at junctions. I think I'll be saving on the petrol – although it may be hundreds, rather than thousands, of pounds ...

The truth and myths about saving petrol

Speed According to the Department for Transport, driving at 70mph uses up to 9% more fuel than at 60mph and up to 15% more than at 50mph. 80mph can use up to 25% more than at 70mph.

Tyres Over time, tyres will naturally leak a bit of air. The RAC says you can improve fuel consumption by up to 2% if you check pressures regularly, and keep them at the correct pressure. It's safer, too – dozens of people a year die because of poorly-inflated tyres.

Roof racks There's enormous disagreement. A report by car manual maker Haynes says get rid of the rack – fully loaded it can add 30% to fuel consumption. But AutoExpress says it's a myth – its test found that those with aerodynamic designs added little to the fuel bill.

Air con vs open windows At low speeds, such as driving around town, air conditioning can add 5%-7% to fuel costs, says Anthony Sale of Millbrook, so just wind the window down. But at higher speeds, the effects are less noticeable.

However, when driving at speed, an open window or sun roof increases aerodynamic drag and can add a further 3-6% to costs, according to some estimates. In 2005, Consumer Reports (the US equivalent to Which?) tested a Honda Accord. Using air conditioning at 65 mph reduced fuel economy by over 3 mpg. Opening the windows on the Honda at 65 mph was not measurable. But US car website edmunds.com found a minimal difference . "Do what's comfortable," it said.

Radio/CD In a survey by BP, 10% of drivers thought that turning off the radio improved fuel consumption. It doesn't.

Engine size Don't assume smaller engines use less petrol. A big car with a 2.0L engine may use less than the same car with a 1.6L engine as it strains to pull a larger weight. On test, a people carrier with a small engine recorded much worse fuel efficiency than one with a bigger engine.

Petrol vs diesel In general, diesels will use less fuel, but, as they typically cost more to buy, the savings aren't always obvious. The Environmental Transport Association has a calculator on its website, that gives you an indication of the costs of running on diesel, petrol, biodiesel, electric battery or fuel cells. Sale says: "I've driven diesels with dreadful fuel efficiency, and petrol cars that have excellent fuel efficiency."

Coasting Rolling downhill or approaching a junction with the car out of gear used to be a common practice to save fuel. But the AA strongly advises against it. "You lose the ability to suddenly accelerate out of tricky situations [and] you lose engine braking ... These days, coasting is still inadvisable and changes in vehicle fuel systems mean it won't save you fuel, either."

Running on chip fat Plenty of cars with older diesel engines can run on vegetable oil – either mixed in with ordinary diesel or, following some modifications, entirely on such oils. It sells for about 55p a litre – less than half the price of standard diesel.

The only downside is the smell that comes out of the exhaust, which has been likened to a fish and chip shop or a barbecue. In 2007 the Treasury relaxed the rules on the taxation of home-made and shop-bought oil, and drivers are no longer required to pay the HM Revenue & Customs fuel duty on 2,500 litres of vegetable oil a year for personal use. Users have to keep all receipts so they can prove they are not using more than 2,500 litres a year if they are stopped in a roadside check.

More details are available at Veg Oil Motoring.

Buying super-unleaded BP says you get around 28 miles extra from a tank of super-unleaded petrol, and that the same results can be achieved whether the car is new or old, high-performance or standard. Using super unleaded also reduces exhaust emissions and deposits in the engine.

But the drawback is that it costs that bit extra – adding at least 4p a litre.

Cheap petrol stations Website PetrolPrices.com gives you the cheapest petrol prices in your area once you have entered your postcode. Men cost more than women. OK, this is stretching it. But as men tend to weigh more than women, they use up more fuel being transported around. Having three men squeezed into the back seats of a car adds.