England should be targeting at least reaching the quarter-finals in Russia, according to the Football Association’s chief executive, Martin Glenn.

Although Gareth Southgate has been guaranteed he will keep his job regardless of how England fare at the World Cup, encouraging performances in two warm-up games have raised expectations.

Glenn said winning a knockout game at a major tournament for the first time since England’s so-called “golden generation” reached the 2006 World Cup quarter-finals would represent a success.

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“I’m going to give it away slightly,” Glenn said. “We haven’t won a knockout game since 2006 so, clearly, getting out of the group and winning a knockout game would be a real sign of progress and, if you win one, you win more.”

He took his post in 2015, in time to see England’s dismal exit from Euro 2016, where they were defeated by Iceland in the round of 16. But he said he was encouraged by the 23-man squad picked by Southgate, which has an average age of 26.

“I think we’ve never been better prepared,” he said. “We’ve got a youngish squad; not the youngest in the tournament but pretty young. And we’ve got a world-class support team, we really have. That level of preparation has been good. We’ve embedded psychological work into the core. Could we be better prepared? Probably not.”

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Glenn also praised the environment inside the England camp which he said may have played a part in Danny Rose revealing he had suffered from depression.

“Obviously if there were any risks we would be all over it. I actually just think his coming out with those concerns speaks really well of the environment of the camp, that he felt comfortable enough to say it.”

The Duke of Cambridge, a patron of Heads Together, a mental health charity, visited the England squad before they defeated Costa Rica at Elland Road.

“Prince William was talking to Danny because the Heads Together charity is a really important thing for him,” Glenn said. “I think it speaks masses for the comfort in the camp for people to be able to come out with things like that and say it. What we try to do is de-stress the camp, make the relationship with the media more open and I suspect that environment probably helped.”