Young drivers who have just passed their test are likely to experience difficultly getting insurance and when they do the premium will almost certainly be expensive.

Over the past couple of years a number of insurance companies have withdrawn cover for young drivers in the face of mounting claims. Axa, More Than, Swiftcover, Saga, Esure, Sheila's Wheels and Halifax are among the growing number that automatically reject all applications from 17-year-olds, although some may consider adding them to a parent's policy in exceptional circumstances.

Concerns are mounting about the high casualty rate among young drivers, with under 21s 10 times more likely to be killed or seriously injured in an accident than those aged 35. A third of all road deaths involve drivers aged 17 to 25.

Many insurers will not offer cover to people who are aged under 21, while in some cases firms will not insure people under 25. According to the AA, fewer than a quarter of insurers offer cover to 17-year-olds.

The AA has warned the lack of choice in the marketplace for young driver car insurance and the rising cost of premiums is in turn encouraging fraud. The organisation is calling on the insurance industry to do more to recognise steps taken by young motorists to improve their driving.

The number of cases of the fraudulent practice of "fronting", when a parent insures a child's car in their own name but adds their child, the real main driver, to the policy in an attempt to keep costs down, has shot up in the past two years.

BBC Top Gear presenters Jeremy Clarkson, Richard Hammond and James May recently landed themselves in hot water after promoting this practice in an episode of the programme. The presenters were challenged to see who could get the cheapest insurance premium for a 17 year old male driver. "It soon dawned on us that the only realistic way of getting covered when you are 17 is by going on your parents' insurance," James May commented. "So we got back on the phones pretending to be dad."

Although May's co-presenter Hammond was quick to add a caveat: "Can I just point out before we do move on; if you do decide to put yourself on your parent's insurance and you have a crash, and the insurance company find out that it wasn't really your car ... they won't pay out, then they can prosecute you and you might go to jail."

Even though fronting is classed as insurance fraud, many parents carry it out without ever realising it is a criminal offence. Nick Starling from the Association of British Insurers said "Anyone who sees insurance as a soft touch can end up with a criminal record, credit problems and costlier and harder-to-obtain insurance."

Young drivers could improve their chances of getting a lower premium by taking "Pass Plus" - six further driving instruction sessions that offer wider experience of motorways, country lanes and night driving. The course can reduce insurance premiums by up to 35%.

Furthermore young drivers should pay significantly less for insurance if they opt for a car with a small engine.

Simon Douglas, director of AA Insurance, said: "Perhaps it's time for greater investment in targeted driver training at a younger age to enable new drivers to get on the road safely and responsibly, help reduce claims and make insurance more affordable."

The AA has recently teamed up with the police to offer free driver safety training to young people who are deemed to be at risk, such as those who have been caught speeding, using mobile phones while driving or not wearing seat belts.

The scheme, called Drive Smart, was launched in north Wales last month and the AA Charitable Trust plans to fund at least 2,000 free courses across the country.