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Alastair Cook feared for his England career before rediscovering his best form as he put Australia to the sword with a sensational, record-breaking innings of 244 not out in the Boxing Day Test.

England closed day three on 491 for nine, a lead of 164. They were unable to add to that on day four as James Anderson went first ball, but Australia head coach Darren Lehmann had said the England opener had almost single-handedly ensured his side’s hopes of completing a series whitewash were now over.

Cook admitted afterwards that, like Stuart Broad, with whom he shared a century stand for the ninth wicket, he knew that a senior player might be the one to pay for the Ashes surrender and acknowledged that his return of 83 runs from six innings before the fourth Test had left him “embarrassed” and “beating himself up”.

But Cook surpassed Viv Richards to make the highest score by a visiting batsman at the MCG and even nudged past Brian Lara into sixth place in the all-time Test run-scorers’ list as he recorded his highest Ashes score and fifth Test double century. In the process, Cook has also given his side a real chance of pressing for victory and salvaging some pride from a tough tour in which they have lost the first three Tests, while cementing his own position at the top of the order.

“You don’t know do you?” Cook said when asked if he thought he could have been dropped for Melbourne. “They would have been entitled to because I had not scored a run since Edgbaston [when he made 243 against West Indies]. That is two games against West Indies, three here and the two warmup games.

“I always feel I have had the backing of the selectors but you’ve still got to deliver and I had not done that on this tour, which was very frustrating. Those doubts are always there and they’ve been beating me up for four or five weeks. But I know I’ve done it before. Last night it [scoring a century] ranked right up there, because it was a kind of feeling like [being in the] lastchance saloon. When you’re in those positions and you dig yourself out, it makes you proud.”

Speaking to BT Sport, he added: “It’s one of those 10 hours where I’ll look back and go, ‘ Yeah, things were working well’. The whole tour I’ve been struggling to get that rhythm and I was a bit embarrassed by my performance, but at least today I’ve got a big one. It’s never going to be pretty, my batting, but sometimes it’s effective.”

Cook was at his most positive, hitting 27 boundaries and only slowing when Australian captain Steve Smith – who dropped him for the second time in as many days – spread the field, giving him singles to get a tail-ender on strike.

His remarkable stamina was on show again, still running quick threes when he was way past his double hundred and after more than 10 hours at the crease.

“He was very impressive and showed the younger guys how you have to grind it out and sometimes work out a different way to make runs in Test cricket,” said Lehmann. Of the potential whitewash, the Australian coach added: “We did not go into the game looking that far ahead but they have taken that opportunity away from us.”

Lehmann also gave little credence to the idea that Australia, Special day: Alastair Cook is greeted by fans as he walks off at the close of play who were 164 runs adrift at the end of the England innings, could bat quickly to set the tourists a target. “We’re 160 runs behind, mate … we’d have to get 450 in a day,” he said. “How do you want us to do that? Full credit to England, we’ve been outplayed by a better side at the moment.”

Cook has had plenty of crises before and he was emotional after securing his hundred on the second evening as the relief washed over him. He batted with a renewed purpose throughout, but it was his concentration that ground down Australia on day three as they tried every field setting in the captaincy manual to try to unsettle his mind.

“With my batting over periods of time there are a lot of moving parts to it so, when it is not sync, it can be frustrating,” he said. “One way of delivering is time in the middle then you start to feel at ease.

“You get a few times in your career when you get into that bit of rhythm and time flies by. On this tour batting for 30 minutes has felt like two hours but the last 10 hours for some reason have gone quickly.”

What hurts Cook is that his top form has come too late in the series. “It is a shame it is three or four weeks too late but I will have to live with that for a long time,” he said. “Most of my runs are pretty ugly and hard work. That has not changed my whole career, but I am proud to work hard and I had an opportunity between games to do the extra work, which is what I needed.

“I have doubted myself for 12 years. The longer it goes the harder it becomes which is why I am proud that I went to the well again and delivered a performance like that.”

He was modest in acknowledging that he had gone past all-time great Lara this innings. “I can’t really explain that. I feel a bit sorry for Brian to be honest. It is a special moment to see your name up there.”