If not, the consequences could prove expensive, particularly if you are involved in an accident or if your car is stolen.
A breakdown requiring recovery from Rome to London, can cost more than pounds 1,000, for instance.
"Even basic roadside assistance can cost an average of pounds 90 when you're abroad," says the RAC.
Staying abroad while your vehicle is repaired is not a cheap solution. Hiring a car for seven days costs pounds 400 on average, while freighting repair parts from the UK could add a further pounds 114 to your final bill.
Personal repatriation due to vehicle breakdown, theft or driver illness is even more costly. A party of four from Rome to London can expect fares of between pounds 800 and pounds 1,200. Should expert medical help and a fully equipped flying ambulance be required, then costs rocket.
Your UK motor-insurance policy will already cover you to drive abroad, but it only provides the minimum cover required by law in the EC region and does not include theft, fire or damage to your vehicle, and may not completely cover your liability to other people. So it's wise to ensure that you have the same level of cover when abroad as you have in the UK.
AA Insurance highlights the fact that one in four insurance companies make a charge to extend cover abroad. On average, this is a flat fee of pounds 21, but some insurers charge as much as pounds 24 plus a 70p a day surcharge, bringing the cost of a two-week trip to pounds 33.80p
Among the cheapest deals at the moment are those offered by Eagle Star Direct and Zurich Municipal, which include 60 days overseas cover in their policies. By contrast, Direct Line charges pounds 31 a month.
"The whole issue is a minefield for the consumer," says AA Insurance man Andrew Howard. He advises policy-holders when comparing general motor premiums from one company to the next, to check that they won't be asked to stump up extra premiums every time they take their car abroad.
The RAC is calling on the insurance industry to issue annual cover for Europe as part of any motoring policy.
Ask your insurer for a Green Card before you go. It provides no cover in itself, but is widely accepted by authorities abroad as cover provided by your policy. The RAC's insurance compliance manager, Nigel Richardson, said: "It's becoming less important to carry a Green Card within the EU, but some countries and some insurers still insist on it or will limit cover to the legal minimum required in the country in which the vehicle is being driven."
The Green Card can also save time and frustration if there is an accident, as police officers throughout Europe can easily recognise it.
The RAC issues 58,000 policies every year, yet still receives calls from British motorists having problems in continental Europe and don't possess comprehensive motoring or personal cover.
Insurance adviser James Wootten stresses the need to examine your policy carefully before the holiday because a policy that appears cheaper than its rivals it can turn out to be more expensive if key benefits that a competitor offers cheaper, or free, are taken into account.
"Most insurance companies will penalise you if you switch mid-year, but if you ask them for extra cover when you renew your policy, you should get an attractive offer and, in many cases, it could be free."