Phil Berry, a manager at AGF Insurance, said anyone aiming to buy a car with 12 months' free insurance should take into account the cost of renewing their insurance a year later.
In some cases, they could be facing unexpected bills of pounds 2,000 or more, he added. Had they known in advance what the likely cost would be they might have chosen to buy another vehicle.
Mr Berry said: 'We are not trying to put anyone off buying a car with a free insurance offer. In many cases this is a particularly worthwhile bonus, all the more so when someone really wants that model.'
He said the problem could be particularly acute where young people on low incomes are tempted to buy high-performance cars. Although free insurance offers have waned in popularity compared to a few years ago, they are still available from several manufacturers. These include Citroen's AX range, plus some Peugeot and Daihatsu models.
An 18-year-old London driver without a no-claims bonus would have to pay pounds 2,800 insurance on a Citroen AX. This assumes a pounds 300 excess on his cover.
A female, 22, living in Manchester, would find herself paying pounds 1,047 to renew her policy on a car in the same range. After five years, premiums would fall to about pounds 600.