Asher-Smith added the 4x100 metres title to her 100m and 200m crowns in Berlin yesterday to become the first Briton to ever win all three at a major championships.
It wrapped up the final evening at the Olympic Stadium after Muir had taken the 1500m title – the first British woman to win the event – with the British men’s sprint relay squad also winning gold.
Asher-Smith anchored the team of Asha Philip, Imani Lansiquot and Bianca Williams to victory in 41.88 seconds, a world-leading time.
Asher-Smith, 22, said: “I came and won everything I entered so I’m very happy. I’m happy, but it’s all about moving to Tokyo (the Olympics in 2020) and you’ve got to use it and push yourself on to a platform.
“The British athletes have had the Commonwealths and Europeans this year, so we’ve had to peak.
“Half the American people aren’t even running. While it’s great for me this year it doesn’t forecast how the next two years are going to go.
“When I got the baton I was like, ‘Not today, today is our day’ and I’m very happy to finish that off for the girls.
“I saw people and thought, ‘Not on my watch’.”
Muir became the first British woman to win the 1500m at the Europeans, adding the title to her 1500m and 3000m European indoor crowns she won last year.
The 25-year-old was overwhelming favourite and won in 4mins 02.32secs after a dominant display of front-running, with team-mate Laura Weightman claiming bronze.
Muir, whose gold was one of seven for the British team in Germany, claimed world indoor silver and bronze in the 1500m and 3000m respectively in March.
She said: “I’ve proved on a European level that I’m one of the best and one of the best in the world. But there are so many bright stars on a GB level.
“Now it’s world’s outdoors (in Doha next year) and Olympics. That’s the next step. But I’m excited for the next few years.
“Me and Sifan (Hassan of Holland, who opted to race the 5,000m in Berlin) have gone back and forth so many times. I’ve won races. She’s won races. Now there is no clear favourite.
“Everyone is winning different races. It’s great to see. Going into any race, there are four or five girls who can win it. That’s exciting, but I’ve shown I can be one of the contenders.”
Muir also told the BBC: “I knew a lot of the girls have a good finish, so I thought the longer I leave it the riskier it would be.
“I know I can run hard from a long way out, so I did that and I saw Laura come with me, it was great to see that 1-2 on the board. I just ran as hard as I could.
“This was probably the most pressure I have been under, it was something new for me, but I think I handled it really well. I’m just thankful for all the support I have had back home and here as well.”
CJ Ujah, Zharnel Hughes, Adam Gemili and Harry Aikines-Aryeetey, a replacement for the injured Nethaneel Mitchell-Blake, stormed to victory in the men’s 4x100m relay to clinch the third British gold of the night.
Hughes added to the individual 100m old he claimed on Tuesday as the squad clocked 37.80s to win ahead of Turkey and Netherlands.
In the women’s 5,000m final Eilish McColgan claimed second after Israel’s Lonah Salpeter appeared to stop with a lap left.
Salpeter was challenging winner Hassan for the lead, but seemed to think the race was over at the bell and slowed down, allowing McColgan to motor past to win silver in 14:53.05. Salpeter came home fourth, only to later be disqualified.
Elsewhere, Swedish 18-year-old Armand Duplantis cleared a world junior record 6.05m to win pole vault gold, and Belarus’ Volha Mazuronak won European marathon gold on Sunday – despite suffering from a nosebleed.
The 29-year-old finished ahead of Clemence Calvin from France and the Czech Republic’s Eva Vrabcova Nyvltova. She clocked two hours 26.22 minutes on the streets of Berlin but had to battle a nose bleed early on.
After stemming the bleeding, Mazuronak also almost went the wrong way with less than a mile remaining.
Marathon world record holder Paula Radcliffe told the BBC: “It’s very unusual, I don’t think I’ve ever seen it, especially in the early stages of a marathon.”
Tracy Barlow was the highest of five British runners, coming 15th.