Accounts filed at Companies House show the company, still owned by 85-year-old Sir Arnold Clark and his family, recorded a near 17% hike in pre-tax profits from £51.76 million to £60.5m in 2012.
New car sales accelerated by 10.3% from 72,538 to 79,979 while used car sales grew 4.6% from 116,994 to 122,398.
Writing in the accounts the directors said like-for-like new car sales had increased by 6%, which was above the industry average.
They said: "The wider new vehicle market was buoyant in 2012 although it is predicted that growth will flatten in the coming year.
"Fleet sales increased by 11.5% which was due to some significant contracts gained in the year."
Used car like-for-like growth came in at 1.2% in what was described as a "relatively stable market".
The accounts show £17.7m was paid out on acquisitions in the year. The largest acquisition during 2012 was the deal for Grangemouth Motor Group, which traded as John R Weir, in August and brought the Mercedes-Benz brand into Arnold Clark for the first time.
In his statement in the accounts Sir Arnold mentioned other acquisitions including Volkswagen sites in Wishaw and Rutherglen plus Vauxhall dealers in the north west of England at Kendal, Morecambe and Blackpool.
The company also invested in a large building in Wolverhampton which will house a bespoke training centre as well as being available for third parties to hire for training and conferences.
A multi-million pound refurbishment of the flagship Ford dealership in Linwood, Renfrewshire, has resulted in record vehicle sales there.
There was also investment into IT infrastructure with the company's website reporting a 49% increase in visitor.
Sir Arnold, chairman, said it had been another successful year for the group in spite of a "very weak" UK economy.
He said: "While the wider economic situation remains uncertain the consensus in the motor industry is for modest growth in both the new and used retail markets.
"Our hard work and impressive results in recent years mean that we are confident about our ability to achieve profitable expansion, both organically and through strategic acquisitions.
"We have laid down strong foundations for growth and are fully committed to achieving our goal of being the UK's pre-eminent motor retailer."
The directors added the early trading results of 2013 gave them confidence about prospects for the year.
They added: "The Board predicts turnover will increase in the coming year and expect profitability to remain at levels similar to 2012."
According to the accounts for 2012 staff costs rose from £197.3m to £203.9m in a year when average employee numbers increased from 8087 to 8315.
Directors' emoluments increased from £4.46m to £5.9m with the highest paid seeing their rewards go up 13% from £1.93m to £2.19m.
The company also formed an operations board - which includes senior representatives from human resources as well as the franchising, leasing, finance and parts divisions - to sit below the main board and improve efficiency.
Sir Arnold said: "The impact of the operations board has already been substantial."
After joining the Royal Air Force as a teenager Sir Arnold later became a motor mechanic instructor.
It was in 1954 when he opened his first car dealership in Glasgow.Having established itself as the biggest car dealer in Scotland the first move into England came with the opening of a site in Liverpool in 1994.
The business is now thought to be the largest privately held motor dealer in Europe.