Sir John, during a tough questioning by the Commons Select Committee on Culture, Media and Sport, said the channel would cost the BBC pounds 53.9m in the current financial year.
Gerald Kaufman, chairman of the committee, claimed that figure was nearly twice as much as had been anticipated. "When BBC News 24 was set up, we expected a cost closer to pounds 30m. How can we justify the increased cost?" he said.
However, defending the need for the overall pounds 650m increase in corporation's funding, Sir John told MPs that six million people watched BBC News 24 on cable every week, more than watched Sky News.
Most of the 1.82 million viewers who receive digital television access the BBC's digital channels as part of pay-TV packages including cable, Sky Digital, and ONdigital, the terrestrial service. Both Sky Digital and ONdigital offer free set-top boxes to viewers subscribing to a package of channels. But 10,000 viewers have bought a pounds 100 set-top box to receive the limited number of free-to-air digital channels.
Greg Dyke, the incoming director general of the BBC, told the committe that the corporation would not be able to compete with Sky Digital over sports coverage.
He said Sky Sports was likely to pay pounds 5m to pounds 6m for each Premier League football match next season. "We cannot justify spending that sort of money. We could produce an eight to 10-part drama series for that," he said. "The rates for sport coverage are going up beyond the BBC's means so we will have be about picking and choosing."
The future funding of the BBC has been the subject of intense debate since a government advisory committee recommended in August that the BBC's expansion into digital services should be funded by a pounds 24-a-year levy on digital viewers. The committee, headed by the economist Gavyn Davies, said the levy would increase the BBC's income by between pounds 150m and pounds 200m a year.
The plans have been widely criticised by commercial broadcasters who fear the levy could discourage people from signing up to digital. Sky, which draws most of its revenue from subscriptions, would prefer to see some BBC digital services - most notably BBC News 24 - funded by advertising.
Chris Smith, the Secretary of State for Culture, Media and Sport, has already announced that private sector consultants will be brought in to conduct a wide-ranging study of the corporation's efficiency savings.
Mr Smith has said that an "objective, non-partisan analysis" was needed to decide an appropriate level of funding for the BBC in the period to 2006.