Those that follow the latter course will, in many cases, find that their effort is richly rewarded. In some cases the price of the policy can go down by more than a third. The ability to find a cheaper policy comes despite the fact that, as many drivers have discovered, their car insurance premiums has gone up considerably in the last few months.
Andrew Ritchie, insurance analyst at the specialist bank, Fox, Pitt & Kelton, says there are two main reasons for the increases, of over 10 per cent, in the price of motor insurance in the last six months.
First, the profits of many insurance companies in 1998 were very disappointing, especially in the private motor insurance market. Ritchie says: "Broker competition and telephone insurer competition have been driving the prices, and thus the profitability, down.
"In response, firms have been putting rates up and are likely to go on doing so, even if it means loss of market share. It has now gotten to the point where they are quite happy to shed unprofitable business."
The second reason for a hike in premiums is the disappearance of two of the lower-cost insurers. Guardian Royal Exchange and Eagle Star were two firms with a reputation for very competitive quotes but they've now been taken over by Zurich and AXA Sun Life respectively. In addition, on 1 July, the Government raised the insurance premium tax (IPT) from 4 per cent to 5 per cent, adding a bit more to the cost.
The picture ahead does not look any better. Ritchie says: "We'll most probably see more rate increases as quoted insurance companies continue to feel the pressure from their shareholders to raise prices."
There might be a feeling of inevitability in the industry about rising premiums, but deals are still there to be had. For instance, a 30-year- old woman driving a 1997 Rover 220SD, and living in Oxford, could pay as little as pounds 199 with Churchill Insurance or as much as pounds 273 with CGU - or pounds 279 if she uses James & Browne Insurance Brokers.
The variation is even wider for a Londoner of 50 with six points on his licence and living in Deptford. For him a comprehensive policy can vary from between as little as pounds 195, again with Churchill, and pounds 317 with the Lloyds broker Highway.
Just because Churchill Insurance could quote the best rate in those two cases, it does not mean that it will be the cheapest in all cases. A lot depends on the driver's individual circumstances, such as gender, place of residence, type of car, driving record and previous history of claims .
Motorists generally get their car insurance through one of two ways: either by going to an insurance broker who will recommend one of the companies he or she represents, or by going to a direct-by-phone seller. The most famous phone insurer is Direct Line, set up in 1985, that undercuts the traditional brokers.
The insurance brokers had no choice but to invest in technology to compete with their speed of service and bring down operating costs. According to Jennifer Weller, spokesperson for the British Insurance and Investment Brokers' Association (Biiba): "Eight times out of 10, brokers will, in fact, outdo direct sellers on price."
Ms Weller advises the broker route over the direct sellers, saying: "I would definitely recommend that motorists go to a broker for their motor insurance because they give you choice; an extra layer of protection in case the insurance company goes bust; bespoke service; and independent advice."
Biiba has over 2,500 brokers on its database and can provide callers with a list of local ones, as well as specialist brokers who can provide insurance for classic cars or people with special circumstances.
The male driver who lives in Deptford and has driving convictions has a more difficult time getting cover. One company, CGU, will not cover him at all because he exceeds their limit of five penalty points. Another, Royal & SunAlliance, was not only unwilling to quote a figure for comprehensive insurance but would not even offer protection against fire or theft. The only policy available to this driver with Royal & SunAlliance was third party.
Eammon Browne, principal at James & Browne Insurance Brokers, would like motorists to focus on more than just the premium quoted for the policy. He says: "Sometimes the cheapest policy is not really the cheapest option when you take into account the needs of the client.
"For instance, a client may have breakdown cover with the AA or the RAC, which he or she is paying for separately. A good broker would know that some insurance companies will offer breakdown cover at a considerable discount." In many cases this will work out at less than pounds 50 for a one- year cover against more than pounds 100 if you go directly to the recovery service company.
In addition, Mr Browne observes that a good broker will know which are the insurance companies with a reputation for putting up all sorts of obstacles when a policyholder has to make a claim.
Pauline Quail, of Chartwell Insurers, a Cheshire-based insurance broker, says: "Although direct insurers have had their day, we are now winning the war as we are proving that we can provide the goods when it comes not only to choice, quality of service - but also price."
Be prepared to negotiate.