The former chairman of the Committee on Standards in Public Life, Sir Alistair Graham, has described Maria Miller's attempts to frustrate the commissioner's inquiry into her expenses claims as "pretty shocking".

Graham said her case showed that the disciplinary procedures for MPs should be reformed.

His comments came after emails disclosed that the culture secretary had threatened parliament's independent standards commissioner, Kathryn Hudson, in an attempt to block the "irrational and perverse" investigation into her expenses claims.

In a sign of Miller's attempts to prevent an investigation into her claims for interest payments on her mortgage, she told Hudson that the commissioner would be acting in a way that was "unwarranted, unfair and contrary to all standards of due process and legality".

Miller, who was ordered on Thursday to apologise for her conduct towards Hudson and to repay £5,800, even threatened to refer the watchdog to the "supervisory jurisdiction" of the Commons standards committee.

Graham told the BBC Radio 4 Today programme: "The degree of lack of co-operation or the attempt to divert the commissioner from addressing the issues concerned seems fairly exceptional.

"I think particularly for a senior cabinet minister, who you expect to show a leadership role in co-operating with whatever expenses system is around, it is pretty shocking.

"I think the public will be very shocked that the committee did overturn one of the key recommendations about how much should be repaid back, when there is a real possibility that the minister made a capital gain with the help of public funds."

Graham and the current chairman of the Committee on Standards in Public Life, Lord Bew, each raised concerns about the makeup and independence of the Commons standards committee.

MPs did not accept a recommendation by the Committee on Standards in Public Life that lay members – appointed to the Commons committee in the wake of the expenses scandal – should have full voting rights.

The three lay members do not have a vote but play a full part in discussions and have the power to append an opinion to any committee report.

In a statement to the Today programme, Bew said: "The committee's expenses inquiry in 2009 looked at the disciplinary systems within the House of Commons and recommended that the membership of the Commons standards and privileges committee should include lay members with full voting rights to better represent the views of the public.

"We are pleased that lay members have been appointed to that committee. However, there remains some debate about whether they will have full voting rights."

Graham said: "I think what the Maria Miller case highlights is the need for further reform, because if you do a comparison between the disciplinary committee system for members of parliament with other professional groups like lawyers, doctors, dentists, opticians, they have an independent lay chair and they have a majority of lay voting members on the committee, supplemented normally by one or two people from the profession itself.

"That seems to be a more appropriate model for the House of Commons. Plus the fact that those hearings are held in public."

Bew declined to comment on Miller's case but said: "At a time when we are beginning to move on from the damaging expenses scandal, parliament really needs to be seen to be listening and not repeating past mistakes."

On Thursday Miller was told by the Commons standards committee, which issues judgments on the watchdog's report, that she would only need to repay £5,800 – a reduction from the £45,000 Hudson recommended that the minister return for overclaimed allowances on her second home in Wimbledon, south-west London.

The Daily Telegraph reported in December 2012 that Miller had claimed more than £90,000 in mortgage interest and other costs for the property in which her parents lived even though parliamentary rules said a second home must be for the exclusive use of MPs.

The property was bought for £234,000 in 1996, but she and her husband subsequently raised a mortgage on it of £525,000.

The decision by the standards committee to decrease the amount suggested by Hudson prompted the Labour MP John Mann, whose complaint caused the inquiry into Miller, to say on Friday night that politicians should no longer act in judgment over themselves.

He told the Guardian: "Self-regulation of MPs by MPs is now well and truly dead. The committee should only exist to look at how parliament can improve standards in public life.

"Instead the independent commissioner should make decisions on MPs with appeals to the independent advisers. And the electorate needs to be give the right of recall for serious offences."