An unpleasant surprise awaits the millions of drivers renewing their insurance over the next few weeks, with premiums expected to rise substantially on the back of changes to the way compensation payments are calculated.

The Government’s decision to alter the formula in the light of continuing low interest rates means insurers will have to pay victims of serious accidents considerably more, a cost they will be eager to pass on.

And it will not be long before motorists feel the pain, as this month’s issue of the year’s first new registration plates marks the beginning of one of the busiest periods for renewals.

Kevin Pratt, consumer affairs expert at price comparison site MoneySuperMarket, said: “The change is much greater than insurers expected, and a lot of scary numbers are flying around regarding the impact on car insurance premiums – insurers are squealing about having to impose annual hikes of £60 or more.

“On top of the 20 per cent increase in insurance premium tax coming in June and the general upward trend in premiums in recent months, motorists are right to be concerned.”

However, drivers do not have to resign themselves to paying more. Matt Oliver, spokesman for Gocompare car insurance, said: “The only way to be sure you get the best price possible for your specific circumstances is to shop around when your renewal comes through.”

The comparison site said that the UK’s motorists waste a combined total of £1.5 billion a year by letting their insurance renew automatically.

Those aged 18 to 24 are the most apathetic, with almost a quarter admitting that they auto-renew. Yet, as those typically facing the highest premiums, they have most to save.

According to Gocompare, just under a third of all drivers have been with their insurer for three years or more, while almost a quarter have stayed for at least four.

When asked why they allowed their cover to auto-renew, three out of ten said that their provider was cheapest last time they checked so they assumed it would be good value this year too.

A similar proportion stayed put because of loyalty, while a further two in ten cited a good experience with a past claim or confessed that they were afraid to switch because they thought it would be difficult.

Mr Oliver said: “Loyalty, when it comes to car insurance, generally doesn’t pay. The best deals nearly always go to new customers.

“Different insurers will always take a slightly different view of you and your car, when it comes to insurance risk. Therefore, when prices are rising, it is more important than ever not to accept the premium your current insurer is offering, but check to see if you can get a better deal elsewhere.

“The savings from shopping around this year could be significant and drivers need to give themselves enough time at renewal to do a proper job, rather than just letting their insurer roll them over for another year.”

The quickest and simplest way to check the alternatives is via comparison websites. They do not all list the same providers, though, so it is worth trying more than one. A few providers, including Aviva and Direct Line, choose not to appear on any, but it is easy to get additional quotes from their own sites.

The whole process should not take more than an hour or so and could save you several hundred pounds.

To get the best possible price, keep your car in a garage or on a private driveway overnight, where it will be less at risk of theft or damage, and ensure it has an approved alarm and immobiliser.

Do not over-estimate your likely annual mileage – use the figure on your latest MOT certificate to make a realistic projection.

Including a partner or parent who might use the car as a named driver could reduce the premium significantly if they have a good record, but do not be tempted to put down the wrong main driver to get cheaper cover as this is a criminal offence.

Opting for a higher voluntary excess – the amount of any claim you pay yourself – may make a substantial difference too, but do not raise it to more than you could comfortably afford.

If your household has more than one vehicle, check if you could save with a multi-car policy. These are open to family members and groups of friends sharing an address, and cars can be added as they become due, each with a different level of cover and excess.

People often assume third-party cover will be cheaper but a fully comprehensive policy could cost less. This is because some insurers think customers who take the highest level care more about their vehicles and will, therefore, drive more carefully.

Paying for the whole year in advance is generally cheaper, as most insurers add interest to monthly payments. If you cannot afford to pay in one go, spread the cost using a credit card with an extended zero interest period.

Before accepting a quote, check the small print to ensure you are comparing like-for-like and that you understand exactly what is and is not covered.

Mr Oliver added: “If you decide to switch, you’ll need to tell your current provider. Most policies automatically renew unless you notify the insurer to the contrary. If you don’t stop the auto-renewal, you could be faced with a hefty cancellation charge.”

If you are buying a new or second-hand car, shopping around can make a significant difference to the price of this too. American Express says the average cost of buying in Scotland is £13,191, compared to a UK average of £11,094.

Instead of heading for the nearest dealership, use the internet to search outside your local area to get the best possible deal. Set a budget for the purchase and research likely running costs for your chosen model to ensure you can afford these too. Then haggle – the prices are rarely set in stone.