Mary Earps had promised the best was yet to come from England after three limp but dogged performances out of four had earned them a place in this quarter-final. In front of 75,784 overwhelmingly hostile fans, they delivered. Well, mostly.

It was far from complete, but it was a huge improvement and the forwards Lauren Hemp and Alessia Russo ensured England came from behind against Colombia to set up a mouthwatering semi-final against the co-hosts Australia on Wednesday.

“We know if we play at our best, we are unstoppable,” Hemp told the BBC regarding the match-up with Australia. “As a group we showed the team that we wanted to be and hopefully in a few days we’ll do that against Australia.”

Stadium Australia was slow to fill, fans staying camped in front of every size and shape of screen available outside the stadium to watch Australia’s dramatic penalty shootout victory over France. It was carnival-like in mood, England fans, Colombia fans and Australians exploding out of the bars and towards the turnstiles the moment Cortnee Vine’s spot-kick struck the back of the net.

Related: England v Colombia: Women’s World Cup quarter-final – live

You would have been forgiven for thinking you were in the centre of Bogotá and not the outskirts of Sydney. Colombia fans dominated the crowd, many having made a 23-hour flight across three oceans, whatever the cost, to watch their team. The crescendo of voices that joined in with the national anthem was spine-tingling.

The Lionesses have played in front of big crowds in competitive games but none as hostile as this in recent years – their 2019 semi-final against the USA in 2019 and the 2015 quarter-final defeat of the hosts Canada perhaps the closest. Here, their early touches were met with a chorus of boos. It made for excellent preparation for a semi-final back here in front of a host nation hopeful of a first major tournament trophy on home soil à la England at the Euros last year.

England and Colombia had met before in the World Cup, the Lionesses coming off the better in a 2-1 group stage win in 2015. Only Lucy Bronze, Alex Greenwood and Jordan Nobbs remain from that squad, which similarly battled their way to the final four, the underdogs then, the favourites now.

England had struggled with the intensity of Nigeria’s pressing game and close marking of Lauren James in the last-16 match, forced to rely on penalties in Brisbane to scrape through, but they started more brightly here.

They went agonisingly close after six minutes, Russo’s blocked header landing at the feet of Hemp, whose shot was stopped before Russo’s follow-up was scrambled clear. It would not have counted though, with Russo offside.

For Colombia, play being allowed to continue before the flag was raised was costly. Their goalkeeper, Catalina Pérez, clattered into the back of the knee of Carolina Arias, forcing the defender to leave the pitch in tears to be replaced by the 18-year-old Ana María Guzmán, who provided a stunning assist in her side’s 1-0 defeat of Jamaica in the previous round.

Sarina Wiegman had stuck with the 3-5-2 that had thrilled against China but was blunted by Nigeria. The only change was Ella Toone coming in for James, who received a two-match suspension for treading on Nigeria’s Michelle Alozie. It was an underwhelming move, Toone having struggled in England’s opening two games before being dropped to make way for James. She struggled to make an impact again, her gait, shoulders slouched and walking away with the ball still in play for England’s equaliser, symptomatic of her frustration.

It was the feisty tie it had promised to be, Colombia having had a pre-tournament friendly against the Republic of Ireland abandoned owing to its physicality. Guzmán was the first to make her presence felt, bodying Hemp before scraping her thumb across the face of Rachel Daly. Neither incident was punished.

Georgia Stanway was lucky not to go into the book just before the half-hour mark for bringing down the 18-year-old wonder-kid Linda Caicedo. It put her on thin ice, as one of three players, along with Hemp and Bronze, who were a booking from missing the semi-final.

Hemp and Russo were particularly involved as England searched for a performance worthy of their title as European champions. However, Colombia broke the deadlock, Leicy Santos toying with Daly after collecting Caicedo’s pass, before sweeping a dipping effort over a caught-out Earps. It was a luscious finish and the crowd enjoyed it.

In the final minute of six added, Colombia would undo their good work, though, Pérez fumbling the ball, allowing Hemp to lash into the empty net. It was scrappy and desperate but so needed for England.

“It was really important to go in half-time level,” said Hemp. “It was a scrappy goal, but we take any that we can. You’ve always got to be alert in the box, especially as a No 9. It was a proper striker’s finish.”

Another, more forgivable, mistake produced the chance from which the Lionesses took the lead just past the hour. Russo clipped the ball between the legs of Daniela Arias from Stanway’s pass before racing free of the defender and lashing low past Pérez. It would be Pérez’s last action, the goalkeeper down on the grass and she was swapped for the 20-year-old Natalia Giraldo.

Russo’s strike was her second World Cup goal and repaid the faith of Wiegman, who has been steadfast in her belief in the forward despite the claims of Daly, the Women’s Super League’s top scorer, and Bethany England, who scored 12 goals in 12 games for Tottenham.

Earps made a good stop from Lorena Bedoya before England weathered a heavy Colombia storm in the final 10 minutes to secure a fifth major semi-final in eight years. It is a remarkable achievement, made even more remarkable given the tournament, which has included favourite after favourite falling.