Car insurance costs rise by up to 20pc for first-time speed offenders

But anyone caught texting, playing games, picking up emails, talking or otherwise fiddling on a hand-held mobile phone will be hammered hard when it comes to renewal, and some could find cover impossible at any price.

Historically, most insurers overlooked a first speeding offence, but according to new research by AA Insurance, that has changed. All insurers on its panel, which includes giants such as Zurich, Axa, Provident, RSA, CIS, Allianz and Lloyds of London, now pump premiums after a first conviction.

This is confirmed by a Moneysupermarket survey, conducted for the Telegraph, which revealed that across the industry drivers aged 40 and above can now expect an automatic premium increase of around 10pc for a three-point speeding offence, while those in their thirties will be hit with an average 15pc hike. Twenty year-olds suffer most and are likely to see the cost of cover leap by an average 22pc.

But anyone convicted of a mobile phone offence, which can also attract just three points on your licence and a similar fine to speeding, can expect to be punished much more harshly by insurers, with premium increases of up to 60pc. Some will refuse to quote at any price.

Aviva's senior motor underwriting manager Nigel Bartram said: "We want to get the message across that mobile phone usage is absolutely not acceptable. Even though it may be treated by the law in a similar way to a speeding fine, we insurers view it very seriously."

Ian Crowder of the AA said: "We have seen a sharp swing in attitude by insurers towards minor offences such as speeding of late. They used to be more relaxed about it, with most ignoring a first offence. But our latest research reveals that all are now loading premiums by up to a quarter even after a first offence."

The market for careful drivers, with a clean licence remains intensely competitive, with premiums largely unchanged since January 2011.

But they are marching ahead for convicted drivers. Once you lose your clean licence, and join the one-in-six motorists with points on their licence, expect bills to soar. With three speeding points on your licence, prepare for your annual insurance to rise with LV= from £645 to £719 for a 20 year-old, with Allianz from £510 to £581 for a 30 year-old, and again with LV= from £392 to £434 for 40 year-olds.

And with more points, the sky's the limit. All ages can expect their premiums to increase by around half with nine speeding points.

Insurers claim they are able to justify this approach because they now have data that accurately correlates minor motor offences with the likelihood of a claim.

Mr Bartram said: "Technology is constantly improving, allowing us to predict risks ever more closely."

For example, a driver with one conviction is 40pc more likely to claim than his brother with a clean licence, according to internal data at RBS Insurance, one of the UK's largest underwriters including Direct Line and Churchill; with up to half claiming within a year of receiving their points.

As their record deteriorates, so the accident rate rises. A driver with two convictions is 18pc more likely to claim than a driver with one offence. A driver with three offences is 110pc more likely to claim than a driver with two.

The industry is using data like this to price more accurately, thereby ending traditional cross-subsidisation, which saw careful drivers subsidising those who were likely to take risks.

LV= Direct managing director Selwyn Fernandes said: "There are plenty of careful drivers out there with clean licences, and these are the customers which all insurers are looking for. We want to reward them for their good behaviour.

"But we all now have our own claims data which consistently shows that even those with a first speeding offence are more likely to go on to make a claim. They should pay for their higher risk."

LV= is among insurers to take a particularly draconian approach to any mobile phone offence, refusing to offer automatic renewal quotes in most cases.

Mr Fernandes said: "We view this offence very seriously. The driver is clearly distracted. He or she may be texting, playing games or picking up emails. They are a risk not just to themselves but to other road users, and we want to send a signal that this behaviour is socially unacceptable.

"So in many cases we will not offer to quote where someone has a mobile phone conviction. But in other cases, where a driver comes to us direct, we may be able to help them, by talking through their situation."

Mr Crowder also pointed out that in the event of an accident, one of the first things police do is run a check to see if a mobile phone was in use.

Mr Bartram added: "We are concerned that in some areas the penalties are light, for offences which we consider extremely serious. Insurers generally will take a stronger line in the hope that this might act as a deterrent and prevent accidents."

A 20 year-old will face an average increase of 62pc from £924 to £1,495 if caught holding a mobile phone, but this could rise 124pc to £2,483 for a more serious offence earning nine points.

A 30 year-old will see his premium rise by 34pc on average for a three-point mobile phone offence, from £516 to £694. A more serious conviction attracting nine points will more than treble the premium to £1,624.

The picture is similar with 40 year-olds. A first mobile offence will see hikes on average by 26pc from £410 to £517, but with nine points it rockets to £1,310.

But different insurers will take a different view depending on overall circumstances and other factors, so it is always worth shopping around. Allianz, for example, will continue to quote after a mobile phone offence, but typically increases premiums by nearly half.

Finally, companies warn not to attempt to conceal convictions, as this could nullify your insurance. They currently estimate that two in 100 applicants lie about their record, and of these one in three are concealing speeding offences.

The insurance industry is working with the licensing authorities to have direct online access to all driving records to stamp out fraud.