Mourners in Edinburgh have shown up in their “tens of thousands” to pay their respects to the Queen, with many queueing for hours overnight.

Lord Ian Duncan, the Deputy Speaker in the House of Lords, said crowds along the Royal Mile were “ten-deep”, while the streets surrounding the historic precinct were equally crammed with people.

“The sheer quantity of individuals moving into Edinburgh today (indicates) that there will be many tens – possibly even hundreds – of thousands of people who will wish to pay their respects to the late Queen,” Lord Duncan told the Australian Broadcasting Corporation’s Radio National programme on Tuesday morning.

“That is an extraordinary outpouring of respect, grief, celebration of an extraordinary woman.

“By goodness, they were ten-deep. They had to stop people trying to get there because it would have become dangerous.

“The streets around (the Royal Mile) were crammed and now, as people wait to walk past the coffin itself, the expectation of the numbers and the sheer quantity of humanity in Edinburgh today is extraordinary.”

While many people were warned to expect a 12-hour wait to see the monarch’s coffin at St Giles’ Cathedral, those who queued overnight said their wait-time was five or six hours.

Gavin Hamilton from Edinburgh told the PA news agency he was informed upon arrival it would likely be 13 hours before he would have the chance to pay respects to the Queen but it soon became apparent the wait would only be five or six hours.

“It took about five and a quarter hours waiting in line to see her,” he said, adding that he made into the cathedral just before 3am.

“There were people in the queue with me who had travelled from Aberdeen, over 100 miles away, to do this. There were thousands of people in line at 12.30am at the start of the queue.

“The people were still (lining up) after 2.50 am when I got into the cathedral.”

Fellow mourner Mitch Stevenson, who queued for just under five hours with his sister, said they were “overwhelmed with the power and emotion of the occasion” after making it into St Giles’ cathedral just after 1am.

The siblings had initially been advised they would likely need to wait 11 hours to see the Queen’s coffin but were not deterred.

“It was a very important occasion for us – we lost our mum earlier this year and she would have loved to have been able to go, so we went for her memory also,” Mr Stevenson told PA.

“We were told (we would need to wait) about 11 hours. We accepted this but later found out it was not the case,” he added. “Some people, including myself, felt it was perhaps a little bit of scaremongering to get the crowd numbers down a bit.”

Members of the public started going into the cathedral at about 6pm on Monday.

Shortly after 6am on Tuesday the Scottish Government said the approximate waiting time was roughly two hours but added that that is expected to lengthen during the morning.

It advised people wishing to join the queue to go prepared and dressed for the weather.