The sought-after registration mark "S1" had been estimated to fetch between £200,000 and £250,000.

The historic plate was the first registration number to be issued in Edinburgh and it belonged to a leading pioneer of motoring.

The auction house Bonhams, founded in 1793, has a good track record of achieving high prices for registration numbers.

In 2005, the company sold registration "1F" for £144,500 and in 2006, it sold "M1" for a previous world record auction price of £331,500.

The mystery bidder thought to be a number plate dealer, who declined to be named, said of the sale: "I believe that number plates in general are a good investment even at this price. The registration number will remain in the UK and will be going on an old red Skoda which will be seen around the Midlands."

The registration number originally belonged to Sir John HA MacDonald, who was the Lord Justice Clerk of Scotland from 1888 to 1919.

Sir John, who foresaw the rapid development of the motor car and the need for a proper road system, was one of the first owners of a car north of the border.

He was also a founding member of the Automobile Club of Great Britain and Ireland, which later became the RAC, and he was the first president of the Scottish Automobile Club.

Motor registration marks were introduced in 1903 and Sir John became the owner of S1 in the same year.

It has been in his family ever since and was revived in 1958 after being allowed to lapse after the Second World War.

Bonhams said the number was the first to be issued in Edinburgh, but the unavailability of certain records meant it was not possible to say whether it was the first one issued in Scotland.