The Labour Party has "betrayed" the British Jewish community by letting Ken Livingstone "off the hook", Theresa May declared as she launched the Conservative local election campaign on Thursday (6 March).

The prime minister's speech came just days after Labour's National Constitutional Committee suspended the former Mayor of London for another year for claiming Nazi leader Adolf Hitler was a supporter of Zionism in the 1930s.

"A Labour Party totally out of touch with the concerns of the British people, which ignores the priorities of local communities and instead indulges its own ideological obsessions," May said.

"A Labour Party which just this week revealed the depths to which it has now sunk, betraying the Jewish community in our country by letting Ken Livingstone off the hook.

"It could not be clearer that the Labour Party is now a long way away from the common, centre ground of British politics today.

"Then we have the Liberal Democrats – whose only interest seems to be in trying to re-run the referendum. And Ukip, who are too divided to stand up for ordinary people."

But Labour leader Jeremy Corbyn has condemned Livingstone as "grossly insensitive" and called on the party's ruling body, the National Executive Committee, to investigation the left-winger's conduct.

"It is deeply disappointing that, despite his long record of standing up to racism, Ken has failed to acknowledge or apologise for the hurt he has caused," Corbyn said.

"Many people are understandably upset that he has continued to make offensive remarks which could open him to further disciplinary action.

"Since initiating the disciplinary process, I have not interfered with it and respect the independence of the party's disciplinary bodies. But Ken's subsequent comments and actions will now be considered by the National Executive Committee after representations from party members."

May's address come just a month before the local and metro mayoral elections on 5 May. The latest national opinion poll from ICM for The Guardian, of more than 2,000 people between 31 March and 2 April, gave the Tories a 18% lead over Labour (43% versus 25%).

Ken Livingstone defends Nazi comments in tube interview Twitter/Justin Cohen