Mr Corbyn attempted to raise a point of order after the prime minister retreated into an attack on the ex-Labour leader at PMQs for the third week in a row.
Mr Streeting could be heard saying “he’s gone senile”, as Sir Lindsay Hoyle rejected Mr Corbyn’s effort to complain.
The shadow health secretary later apologised, saying on Twitter the Commons comment was made “in jest, but I accept in poor taste”.
He added: “I’ve dropped Jeremy a note directly to apologise for any offence caused.”
Mr Corbyn later used a debate to say he was living “rent-free” in Mr Sunak’s head – accusing the PM of breaking conventions by failing to inform him in advance of his attack.
Sir Keir said Mr Williamson’ short-lived stint in the Sunak government showed how “weak” he was – questioning in judgement in appointing unsuitable ministers.
Mr PM replied: “He talks about judgement, about putting people round the cabinet table. I would just gently remind him that he though [Mr Corbyn] was the right person to look after our security.”
Mr Corbyn later challenged Mr Sunak – saying the prime minister must inform him in advance if he plans to keep bringing him up in the Commons.
“I’m grateful for my continued rent-free tenancy in the prime minister’s head,” the left-winger said. He added: “But in future if he could just let me know when he intends to speak about me, that would be helpful – that’s the norm in the House.”
Mr Sunak responded: “If he could ask [Starmer] to give me advance sight of his questions, I’d be happy to will let him know if I need to bring him up on questions of security.”
The MP for Islington North tried to raise a point of order at the end of PMQs.
But he was shot down by Speaker Sir Lindsay Hoyle, who said the Commons business had moved on to a statement about the Cop27 climate summit.
In jest, but I accept in poor taste. I’ve dropped Jeremy a note directly to apologise for any offence caused.
— Wes Streeting MP (@wesstreeting) November 9, 2022
Mr Corbyn previously criticised Mr Sunak for giving a “wholly inaccurate representation” of his agenda on national security during last week’s PMQs, asking the PM to correct the record.
Tory Commons leader Penny Mordaunt accepted the need for MPs to give each other notice if they plan to refer to them in statements in the House.
But she added: “If he’d like to help correct the record he could publish the manifesto that he stood on, which would have weakened this country and dismantled Nato.”
Mr Corbyn currently sits as an independent, having been suspended by Labour over his response to the Equality and Human Rights Commission (EHRC)’s report into antisemitism in the party.
Earlier this week Sir Keir denied a “purge” of left-wing Labour candidates was under way, insisting his party is “united” amid accusations that some were being blocked from standing at the next general election.
The Labour leader told broadcasters: “We are preparing for the next election, the sooner the better … We are making sure we have got the very best candidates to put before the public for that general election which we so desperately need.”