David Cameron is standing down after six years as British prime minister after his final one-to-one audience with the Queen at Buckingham Palace.

Theresa May will tonight arrive at Number Ten Downing Street as Cameron's successor after her own meeting with Her Majesty. She is expected to form her first Cabinet overnight and tomorrow.

Earlier, Cameron bowed out of British politics with his final round of prime minister's questions, after which he received applause from around the House of Commons and a standing ovation on his own side.

After a colourful session, Cameron said he would be "willing on" all politicians and Parliament.

"I will watch these exchanges from the back benches. I will miss the roar of the crowd, I will miss the barbs from the opposition, but I will be willing you on," he said.

"And when I say willing you on, I don't just mean willing on the new prime minister at this despatch box, or indeed just willing on the front bench defending the manifesto that I helped put together. But I mean willing all of you on, because people come here with huge passion for the issues they are about. They come here with great love for the constituencies that they represent. And also willing on this place. Because, yes, we can be pretty tough and test and challenge our leaders - perhaps more than some other countries – but that is something we should be proud of and we should keep at it, and I hope you will all keep at it, and I will will you on as you do.

Veteran Tory MP Kenneth Clarke, who ran against Cameron to be leader in 2005, asked the outgoing prime minister his final question, praising his "statesmanlike" leadership and pleading with him to stay on the green benches at a time when "no two people know what Brexit means".

Cameron pointed out that Clarke's first achievement on becoming Chancellor was to fire Cameron as a special advisor and joked about Clarke being notoriously difficult to get hold of. "Tory modernisation never quite got as far as getting Ken Clarke to have a mobile phone," he said.

Cameron began by saying that after his audience with the Queen, "the diary for the rest of my day is remarkably light".

Then in a boisterous and humourous PMQs, Jeremy Corbyn, the embattled Labour leader, thanked Cameron "for his service" and thanked his mother for advice relayed by Cameron earlier this year on how Corbyn should smarten up. Cameron said Corbyn looked "splendid" today.

On Corbyn's leadership, Cameron – who has previously told Corbyn "for God's sake man, go" – said he was "beginning to admire [Corbyn's] tenacity".

Cameron at one point took the opportunity to deny rumours that he did not "love" Larry the Downing Street cat, producing a photograph of himself with the cat.

He also joked that when he was leader of the Opposition while in New York no-one recognised him until someone came up to him and said "Hey Cameron, PMQs, love your show".

Cameron ended the session by saying: "The last thing I would say is that you can achieve a lot of things in politics. You can get a lot of things done. And that in the end, the public service, the national interest, that is what it is all about. Nothing is really impossible if you put your mind to it. After all, as I once said, I was the future once."

The Speaker, John Bercow led the applause for Cameron despite the two men having a testing relationship over the years.