LONDON — Opponents of Jeremy Corbyn, the left-wing leader of Britain’s Labour Party, usually claim one of two things about him: that his politics are extreme and will lead the party to electoral oblivion, or that his values are admirable but he is too incompetent to put them into effect.

These two arguments seem contradictory, but in Mr. Corbyn’s handling of an anti-Semitism scandal that has hung over the Labour Party, they have converged. In April, after months of accusations of anti-Semitism among party members, particularly on social media, Mr. Corbyn ordered an inquiry and asked Shami Chakrabarti, who had just stepped down as the director of Britain’s leading civil liberties organization, Liberty, to head it. So far, so good.

The aftermath of her report, however, has aggravated the very wounds it was supposed to heal. It was inauspicious that, at the news conference in June for its publication, Mr. Corbyn looked on in silence as one of his supporters accused Ruth Smeeth, a Jewish member of Parliament, of conspiring against the party leader. Ms. Smeeth left the room in tears.

Worse followed when, a few weeks later, Mr. Corbyn broke his vow not to create any new members of the House of Lords by nominating Ms. Chakrabarti for a peerage. Whatever justification there might be for this award, it gave the impression of a quid pro quo: that Mr. Corbyn was willing to compromise his lifelong hostility to Britain’s system of unelected privilege in return for an inquiry that pulled its punches.