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Crowds gathered in London's Leicester Square and George Square in Glasgow following Scotland's 0-0 draw with England.
Scotland fans have been celebrating the result, which keeps alive hopes they could still qualify for the next round of the Euro 2020 tournament.
There was large police presence in both cities, and in London 18 men were arrested , the Met Police said.
Most arrests were made in central London and near Wembley Stadium.
The force said offences included violence and disorder, possession of drugs, possession of an offensive weapon (a knuckle duster), racial aggravation, drunk and disorderly behaviour and assault of a police officer, who suffered minor injuries.
When a "large" crowd gathered in Leicester Square, flares were set off as fans, many wearing kilts and draped in Scotland flags, sang Flower of Scotland and chanted "No Scotland, no party".
Thousands of supporters travelled south for the match despite being urged not to unless they had a ticket or had organised somewhere to watch the game.
Earlier a dispersal order was issued for central London , giving police extra powers to break up groups of people where they believe their behaviour is causing a nuisance, harassment or distress.
There was no indication of disorder in George Square but unauthorised large gatherings are prohibited in Scotland under Covid rules.
Scotland's First Minister, Nicola Sturgeon, had urged fans to "be respectful to our hosts" in London and not to behave in any way that was going to make the Covid problem worse.
The 3,000 strong crowd of supporters watching the match at Glasgow's fan zone erupted into huge cheers when the final whistle went on the 0-0 draw.
And at Wembley the Scotland players lapped up the applause of the Tartan Army who stayed behind to celebrate the result as the England fans left.
A fan zone in Trafalgar Square - where Scotland fans traditionally congregate when their team faces the Auld Enemy - was reserved for 750 key workers.
Malcolm Gillespie, from Falkirk but living in London, was one of those who managed to secure a space in the area.
He said the draw was an "amazing" result for Scotland.
The 41-year-old, who attended with his son Santiago, eight, said: "I'm happy but I definitely think we could have edged a win. They've played really well.
"It's been fantastic, a really nice atmosphere. I spoke to some English fans who were really friendly. We've loved every minute of it."
Mark Cumberworth, 58 and from Essex, said he was disappointed in the result, adding: "It's almost like we've settled for a draw, which isn't worst result in the world.
"Scotland have played well. England have no chance [of winning the Euros] playing like this."
The Scotland National Team tweeted that it had been a "monumental" effort from "every one" of the team.
And Nicola Sturgeon tweeted: "Yes, sir, you all boogied."
It was a reference to a video of ecstatic Scotland players dancing to the 1970s disco classic went viral when they clinched qualification for the tournament by defeating Serbia on penalties in November.
The BBC is not responsible for the content of external sites. View original tweet on TwitterSNP Westminster leader Ian Blackford tweeted : "An excellent performance by #Sco - desire, application, organisation and a decent amount of skilful invention.
"On another night we might have taken three points not one. Win on Tuesday and we can stay in #EURO2020 Well done @ScotlandNT. You have done Scotland proud."
London Mayor Sadiq Khan, who attended the match at Wembley, tweeted: "A fair result given the determination on both sides.
"Scotland held that line and made us work for the point."
The result comes off the back of Scotland's 2-0 loss to the Czech Republic on Monday and England defeating Croatia 1-0 the previous day.
Scotland will face Croatia at Hampden on 22 June.
Wembley and Hampden are among 11 venues across Europe hosting the games in the tournament, which was delayed for a year because of the pandemic.
Scotland's men have never made it past the group stage before, but the top two - or possibly three - teams will go through to the knockout phase.
Wembley was open at 25% capacity for the match , with supporters having to show either proof of vaccination or a negative lateral flow test before entry.
The Tartan Army were allocated only about 2,600 tickets for Wembley, due to Covid rules.
In the absence of access to the stadium or official fan zones, many supporters instead booked to watch the match from pubs and bars across London.
Some gathered in Hyde Park and Leicester Square throughout the day, with police moving Scotland fans on from the square during the second half of the match.
It is understood it came after an opposing group tried to approach the visiting fans.
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