The ugliness of the Labour party resorting to the tactics of non-disclosure agreements (NDAs), akin to those seeking to cover up wrongdoing in big business, or sexual harassment by the powerful, is the stark new element in this ongoing story.

The recent Williamson, Willsman and Campbell cases demonstrate that the party’s disciplinary process is shot to pieces

I don’t know what BBC’s Panorama programme tomorrow about Labour and antisemitism will show – but the recent Williamson, Willsman and Campbell cases already demonstrate in varying ways that the Labour party’s disciplinary process is shot to pieces. No one can have confidence that the process is fair, independent of the leadership or, most importantly of all, that it reflects the values of the party. Today we saw three Labour peers quit over the handling of antisemitism cases.

A disciplinary process that regards antisemitism as an appalling evil that has to be rooted out could not have concluded that the correct way to deal with Chris Williamson was let him back into the party with a reprimand – and without referring the case to a full disciplinary hearing – despite his claims that Labour had been “too apologetic” about antisemitism in the party. The process which produced that result must have been interfered with – or isn’t worth the paper it is printed on.

Pete Willsman is a member of the Labour party’s ruling body, the NEC. On 31 May, LBC published a recording of a conversation in which Willsman said problems of antisemitism within Labour had been whipped up by someone in the Israeli embassy: such allegations are profoundly antisemitic.

If Pete Willsman remains a member of the NEC, it is impossible to see how any Jewish person could have confidence that complaints of antisemitism would be dealt with properly. Willsman has been suspended, but otherwise his case has made no progress. I have said that the issue could, and should, have been dealt with within 14 days. There is almost certainly no dispute about what he said.

Willsman, meanwhile, should be given an opportunity to make any representations he wants to the disciplinary body which is deciding whether he is guilty of antisemitism. That process does not require him to be given any significant length of time to prepare or make representations. And because he is on the ruling body of the party, dealing with his case is urgent to restore confidence.

Play Video 0:41 Chris Williamson says Labour has been 'too apologetic' about antisemitism – video

In late May, meanwhile, Alastair Campbell received an email throwing him out of the Labour party, after giving interviews in which he said he had voted for the Lib Dems in the European elections. The process took little more than two days.

Subsequently, shadow attorney general Shami Chakrabarti and a Labour spokesperson both made clear that voting for another party did not constitute grounds for expulsion. But when it wants to, the Labour party will move like the wind to carry out disciplinary proceedings – and when it wants to bury a disciplinary process, it will move like a glacier.

The slow progress of the Williamson case speaks of interference, just as the Willsman case involves delay no doubt in the hope of burying it – yet the speed of the Campbell case features misuse of the rules to get at the leadership’s enemies.

Each of these cases will have to be looked at by the Equality and Human Rights Commission investigators. The conclusions they reach will throw a great light on what has been happening.

Campbell’s expulsion is not an issue of antisemitism – but seeing how swiftly the party acted there shows what could have been done in the antisemitism cases if the will and determination were there.

My horror that Labour was not dealing with antisemitism properly led me in recent months to seek to make the party’s disciplinary process work fairly, independently of the leadership and in a way which reflected our values. The party machine needed leadership to make the process work.

Three Labour peers quit over handling of antisemitism cases Read more

Now something much more radical is required. I had not previously been in favour of a disciplinary process independent of the Labour party, because the party should set its own standards and enforce them. Now it is inevitable and necessary. This means the party will lose control of aspects of the process and show it cannot identify conduct it says it abhors.

But that is a price which will have to be paid to root out evil and restore confidence that the party has some effective method of setting standards.

This can’t wait until the EHRC investigation into antisemitism in the Labour party, which might be six months or more. We need to sit down now and devise a system where disciplinary matters are handled by a body which is independent of the party.

Now, there are no alternatives.

• Charles Falconer is a former lord chancellor, secretary of state for constitutional affairs and secretary of state for justice