Deeper vetting of Andy Coulson would have been unlikely to reveal significant information about his alleged involvement in phone hacking, the UK's former top civil servant has said.

Lord O'Donnell also said that when Mr Coulson entered Downing Street as director of communications in 2010, he signed a form declaring his financial interests without including £40,000 in News Corporation stock.

The comments came as the peer - who retired at the end of last year - gave evidence to the Leveson Inquiry about the role of special advisers in government.

Questions have been raised about why Mr Coulson was cleared only to SC level in No 10, rather than the tougher DV level.

But Lord O'Donnell said he had been keen to keep the numbers of people given the highest vetting to a minimum, to help avoid leaks.

He stressed that SC clearance allowed Mr Coulson to see some secret documents, and it was only after a terrorist incident at East Midlands airport that it was decided he needed to be upgraded. The ex-News of the World editor resigned before the process was complete.

He also pointed out that DV was designed to establish "whether you are blackmailable... in terms of your position or your personal life".

"It would not have gone into enormous detail about phone hacking, for example," Lord O'Donnell said.

The peer was asked about Mr Coulson's admission to the inquiry last week that, while he sold other shares, he held around £40,000 in restricted News Corp stock during his time in Downing Street.

"There is a form which has to be signed which should disclose shareholdings," Lord O'Donnell said. "A form was signed (by Mr Coulson) but it did not disclose the shareholding and it should have done."