Alastair Cook said selectors would have been entitled to drop him over his poor form – before his masterful double-century put England in a winning position in the fourth Ashes Test.

The unflappable opening batsman crushed Australia’s hopes of sweeping the five-Test series with an unbeaten 244 on Thursday to put the tourists 164 runs ahead of Australia with two days left.

The Ashes is already gone after England lost the opening three Tests, with Cook contributing with just 83 runs in six innings. But he made at least partial amends with his towering double-century.

Cook, 33, said he would have understood being dropped, but he bounced back in the Boxing Day Test to present his team with a chance of victory. “[They] would have been entitled just because I literally hadn’t scored a run since Edgbaston,” Cook said, referring to his 243 against the West Indies in August.

“I always feel I’ve got the backing of the selectors but you’ve still got to deliver the goods, I hadn’t done that on this tour. It was very frustrating.”

At the close, Cook had been at the crease for 634 minutes and faced 409 balls to deny the Australians despite being dropped twice on 66 and 153 by Steve Smith. Cook broke a number of records along the way. He surpassed the highest score by a visiting batsman in a Melbourne Test, bettering the 208 by West Indian great Viv Richards in 1984.

He earlier went past Wally Hammond’s 200 set back in 1928 as the highest Test score at the MCG by an Englishman. Cook’s fifth double-century also catapulted him above West Indian Brian Lara to become the sixth highest run-getter in Test cricket with 11,956.

All the emotions came out

“It’s probably been one of the more emotional [ones] from where I’d been on this tour,” Cook admitted. It meant a lot last night and then today I was quite proud that I managed to back it up. After all the emotion came out yesterday, to get a real big one for the team was really important.

“I’ve doubted myself for 12 years and I’ll probably continue to doubt myself but obviously the longer it goes the harder it becomes.

“But I suppose that’s why I can be quite proud of going to the well again and delivering a performance like that was pleasing. It’s just a shame it’s three or four weeks too late, I’ll have to live with that for a long time but it’s nice to score a few.”

The former captain, 33, said he had been working hard in the nets to recapture form and felt he had re-discovered his scoring rhythm. “I’ve always worked hard on my whole game and my approach to cricket, so unfortunately most of my runs are pretty ugly runs and quite hard work – that hasn’t changed throughout my whole career,” he said.

“Obviously, with my batting over a period of time, there are quite a few moving parts to it. When they’re not quite in sync it can be quite frustrating.”

Cook said he had been given great support by the England team during his barren run before posting his 32nd Test century in his 151st Test match. “The feeling when I walked into the change room last night was very special, and obviously today as well,” he said. “The team has been fantastic. Obviously, we’ve had an interesting journey on this tour with a lot of things going on.

“But we’ve stuck together really well as a side and as a group of players and we’ve put in three good days of performance here and let’s hope we can do the same on day four tomorrow.”