Sir Christopher does not expect to report until the autumn
The official inquiry into MPs' expenses has begun work at Westminster - as Tory Ian Taylor became the latest MP to say he was quitting at the next election.
The Committee of Standards in Public Life is holding a series of hearings before recommending changes to expenses and allowances rules later this year.
Chairman Sir Christopher Kelly said the existing system appears to have been "exploited for personal gain".
Commons leader Harriet Harman was among the first to be grilled by the panel.
She told the inquiry plans for a new body to run the MPs' expenses system will be published within a month.
A bill will create the "Parliamentary Standards Authority", which will replace the Commons' fees office, fix MPs' allowances and deal with complaints.
Ms Harman told the inquiry that it should be a "straightforward first step to reforming the discredited system".
She also criticised MPs who had second jobs, such as barristers or bankers in addition to their duties in the House.
She said it dated back to the days when the Commons was a "gentleman's club", adding: "You'd work during the day, and then, a bit of light legislation and dinner in the evening - we should have moved on from that."
Sir Christopher said it was the committee's task to design a new set of rules that would support MPs and restore what he called "shattered trust".
"There can be no doubt about the extent of public anger at the way in which arrangements.
"The reimbursements to MPs of the expenses they necessarily incurred in performing their public duties have been exploited for personal gain.
"Those feelings are shared by many MPs as well."
He said his committee would be guided by "the seven principles of public life: honesty, integrity, openness and others with which people will be familiar".
He added: "These values are timeless - if they had been followed more by more MPs in the last few years we'd not now be in the situation we are."
Sir Christopher has resisted pressure to report earlier than his planned autumn date.
He told BBC One's Andrew Marr show that his committee had been looking at investigation expenses for some time but he had been "both surprised and I think it is fair to say, shocked" by the abuses uncovered by The Daily Telegraph.
The Commons authorities had long fought attempts to release detailed breakdowns of MPs' claims under their controversial second homes allowance - but had been forced to compile receipts after losing a High Court battle under the Freedom of Information Act.
But before they could be published widely, the Daily Telegraph got hold of copies of millions of receipts and began publishing stories about claims by MPs from all parties.
The fallout and public anger has led to money being paid back, MPs announcing they will step down and has been blamed in part for Labour's disastrous showing at the European and English council elections last week.
Esher and Walton MP Ian Taylor has announced he is stepping down, saying there were "several factors" behind his decision - including local opposition to him having a second home in London rather than commuting to Westminster from his Surrey constituency.