England showed they are real contenders to win a second international tournament of the summer after a clinical performance against the hosts booked a place in the semi-finals of the European Under-21 Championship for the first time since 2009.

Goals from Demarai Gray, Jacob Murphy and a late penalty from Lewis Baker capped an excellent display that means Aidy Boothroyd’s side have recovered from a slow start and ended up topping group A with seven points.

England v Poland: European Under-21 Championship – as it happened Read more

It was not supposed to be this easy but after the Under-20 side’s World Cup-winning exploits this month, there is now a sense that anything is possible having seemed down and out at half-time of their second match, against Slovakia.

“It’s good to progress but the job’s not over, we are focused on the semi-finals,” said Gray, who capped a man-of-the-match performance with the assist for Murphy’s crucial second goal. “Can we go further? Why not? We will cause any team problems.”

The Young Lions will have to wait until Saturday night to discover who they will face after Slovakia beat Sweden 3-0 in the group’s other match, with a meeting with Germany the most likely scenario. However, after the embarrassment of departing this tournament at the group stage for the last three editions, England will not be concerned by that just yet.

Boothroyd had opted to give Gray his first start in the tournament in attack alongside Nathan Redmond after deciding not to risk Tammy Abraham from the start. The comeback victory against Slovakia on Monday appeared to have breathed some confidence into the England ranks, with the defender Alfie Mawson admitting that a heated dressing-room argument at the interval had inspired the turnaround. There was certainly evidence of a renewed vigour as they pressed forward in the opening exchanges against a Poland side who scored within the first five minutes of their matches against Slovakia and Sweden yet only had a point to show for it.

Gray, who is believed to be considering his future at Leicester City after a season of limited opportunities, gave England the perfect start in the sixth minute. A surging run from his club-mate Ben Chilwell found the former Birmingham forward in acres of space 25 yards out and his shot took a deflection off Jaroslav Jach’s head to divert past the goalkeeper.

A groin injury to Nathaniel Chalobah then forced Boothroyd into a change, with Derby County’s Will Hughes replacing him as England switched to a three-man central midfield. The Chelsea midfielder may struggle to make the semi-final, given the way he limped away after the match, with doubts also over Redmond after he was substituted at the break by Murphy.

Roared on by a noisy home crowd, Poland had offered little threat going forward until the 69th minute but almost created an opportunity that would have handed them a lifeline. Within seconds, however, a quick break from Gray led to him setting up Murphy for the simplest of tap-ins and England were home and dry.

Facebook Twitter Pinterest Jacob Murphy scores the second goal for England Under-21s. Photograph: Nick Potts/PA

Baker’s late penalty after Abraham was brought down in the box and Jan Bednarek was shown a red card put the seal on a memorable night that means Boothroyd’s side now have four days to prepare for their semi-final.

“I was really pleased with how we coped with the occasion,” said the former Watford manager, who replaced Gareth Southgate when he was promoted to the senior side in September. “It was going to be a partisan crowd and I thought their supporters were brilliant from start to finish. They were singing and made it difficult for us but the early goal settled us. It was certainly a tough game. We seem to be growing in confidence, which is good. We don’t want to peak too early.”

The injuries to two of his most experienced players will be a major concern before the semi-final, although Boothroyd believes the confidence his side have displayed in ending a dismal run of results at previous tournaments should stand them in good stead.

“They both just felt tweaks and it was a decision I had to make, whether I kept them on or changed it around,” he said. “Thankfully the lads who came on did really, really well. I have got a full squad to pick from but we will know more in the morning.

“I believed we could get to the semi-finals,” Boothroyd added, “and we have got there. I think we are getting better and better. When you have a team like that, one that has got momentum and keeps clean sheets, you have got half a chance.”