The coach crashed on a school trip

Father and son William and David Allan, who own Allan's Coaches, said they had also been unsure about the hours drivers should work.

However, they denied tampering with tachographs to disguise the amount of hours drivers were working and their breaks.

Katherine Fish, 15, died and 20 others were injured when an Allan's coach taking pupils from Largs Academy in Ayrshire crashed near Dijon, in France, in June last year.

The company, which is based in Gorebridge, Midlothian, has become the subject of an investigation by the Traffic Commissioner, Joan Aitken.

The inquiry is separate from any investigation into the crash but the commissioner has the power to withdraw an operator's licence.

Mark Chisholm, who was driving the coach which crashed, is still to stand trial in France.

Main carer

William Allan, who was under examination by his solicitor, Michael Whiteford, conceded that the system for collecting tachograph records was "not adequate".

However, he said there were problems following the death of his father and his wife suffered a stroke six years ago.

He became her main carer and gave day-to-day responsibility for matters including tachographs and drivers' schedules to his son David.

Mr Whiteford said: "This must have put pressure on David, to run the whole business."

Mr Allan agreed with this.

Mr Whiteford asked: "Is it your position that you accept that what this (inquiry) has revealed is a lack of training of drivers, a lack of proper checking of tachographs, a system which clearly needed, at that time, a radical improvement?"

"That's right," he replied.

William Allan denied there had been any attempt to falsify the records.

Katherine Fish died in the crash

However, when advocate Mark Lindsay asked him whether the company had so far introduced any changes to the way it monitors tachographs, he said it had not.

David Allan also said that there had been mistakes in the way records had been kept at the company, but denied any intention to tamper with them.

Like his father, he agreed his knowledge of the law on drivers' working hours could be improved, but added that he was going on a course to address this.

The inquiry got under way last week after a probe into the company's operations last summer, which uncovered alleged breaches committed between May and July 2002.