Alastair Cook struck a brilliant double hundred as England assumed a dominant position after three days of the fourth Ashes Test in Melbourne.

Resuming on his overnight score of 104, Cook was rarely troubled as he batted through the day to end on 244 not out from 409 balls at stumps – the highest score by a visiting batsman at the MCG.

Steve Smith, who dropped Cook when he was on 66 on day two, dropped him again on 153, with the 33-year-old making the hosts pay dearly for the blunders.

The England opener shared century partnerships with Joe Root (68) and Stuart Broad (56) in a marathon 10-and-a-half-hour innings to guide England to 491-9 at the close – a lead of 164.

Australia's bowling trio of Josh Hazlewood, Pat Cummins and Nathan Lyon took three wickets apiece, but Jackson Bird struggled to create any sort of sustained pressure on England's batsmen as he ended the day with figures of 0-108 from 30 overs.

The hosts bowled with purpose at the start of the day and were lifted when Root miscued a pull shot to Lyon at deep square leg off Hazlewood.

Controversy arose as Dawid Malan mystifyingly failed to review after he was given out lbw on 14, despite television replays showing that he had inside-edged Hazlewood's delivery.

Lyon then removed Jonny Bairstow (22) and Moeen Ali (20), before Broad provided able support to Cook to allow him to reach his double hundred.

The veteran opener moved to sixth place in the all-time highest run-scorers list in Test cricket with 11,956 runs during the course of his innings, surpassing Mahela Jayawardene, Shivnarine Chanderpaul and Brian Lara.

"Getting a hundred didn't count for much unless I backed it up today. At Perth, I said I was embarrassed. I know it is late but it is nice to contribute to a good day," Cook told BBC Test Match Special.

"In all three games we have put Australia under pressure in two or three sessions and we haven't been able to back it up. Here, even halfway through the afternoon, we were in danger of only getting a 60-run lead and I thought we needed more than that.

"Broady played really well. It was good to have bit of a partnership to get us up to a good lead."

Australia coach Darren Lehmann said the hosts can still win the match but conceded that his side were up against it.

"The batters have got to stand up and it is a great challenge for them," he told ABC. "You never say never but we are a long way behind in the game. It is tough to see a scenario other than a draw or an England win."

Australia have already regained the Ashes and hold an unassailable 3-0 lead in the five-match series.