The Royal Society for the Prevention of Accidents said it was concerning that drivers with 12 points or more were still allowed on the roads.
If a driver reaches this threshold they face a disqualification of at least six months, unless the court accepts that 'exceptional hardship', such as job loss, would be caused.
Driver and Vehicle Licensing Agency data shows this applied to 25 drivers with a Scarborough postcode in March.
And there were almost 11,000 such drivers across Great Britain – though this was a 4% drop on the same point last year.
One driver, a 41-year-old woman from Brighton and Hove, had even received 68 points on her license – the most in the country.
In Scarborough, one driver managed to rack up 18 points.
The data is recorded by postcode district, so some drivers could live just across the border in neighbouring local authority areas.
Safety charity Rospa said it was concerned that there are so many drivers with speeding convictions in the country.
Nick Lloyd, the organisation's head of road safety, added: “More concerning is that a proportion of these drivers, despite having accumulated 12 points or more on their licence, are still on our roads.
"Unfortunately some drivers either intentionally or unintentionally drive above the speed limit, thereby placing themselves, their passengers and other road users in danger."
The DVLA figures show there are 102,185 drivers with full or provisional licences in Scarborough, with a combined 29,742 points between them.
Across Great Britain, 2.7 million drivers, aged between 15 and 102, have at least one point on their licence.
Road safety charity Brake said the law should be used to its fullest extent when dealing with "selfish" speeders.
Joshua Harris, director of campaigns, said: "There is no justification for travelling over the speed limit, especially as people should still be minimising their journeys in lockdown.
"It is extremely important that all drivers recognise that speed limits exist to help save lives and that any crash add burden to our stretched emergency services and NHS."
The Sentencing Council recently concluded a consultation on driving offences disqualifications, with revised guidelines set to be published later this year.
Chairman Lord Justice Holroyde said: “The Council is aware of public concern that offenders who have incurred 12 penalty points or more are not always disqualified from driving.
"There are legitimate reasons why this might happen: the law allows for such a disqualification to be avoided or reduced for reasons of exceptional hardship."
A Government spokesman said: “Speeding puts the lives of drivers and others at risk, putting needless pressure on our emergency services which should be focused on helping the nation battle Covid-19.
“The presence of a valid driving entitlement does not mean that all individuals are actively driving in the UK, and these statistics include cases where drivers have rightly been punished for the breaking the law, and have received court sentences including disqualification, supervision orders, community orders or imprisonment.”
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