Those waiting in the queue, which now has its own BBC weather forecast, faced temperatures of 7C just before 7am on Saturday, at which time the official queue tracker advised the public not to make the journey.
Despite regularly checking the tracker, mourners went against advice to travel to pay their respects to the late monarch.
London Ambulance Service figures showed in the 12 hours to midnight on Friday evening, 275 people were treated, of which 39 were taken to hospital.
Claire Smart, 47, who had come to the capital from Teesside, told the PA news agency she had travelled to “pay my respects and to apologise for all the times as a little girl I rolled my eyes having to listen to the Queen”.
She went on: “I always wanted to curtsy in front of the Queen when she was alive, and sort of felt it was important to come and do it now.”
When asked whether she was put off by the predicted waiting times when she set off at 4.45am, Ms Smart replied: “I just thought I’ll regret not trying.”
Linda Partridge, 71, and Simon Hopkins, 59, travelled from the West Midlands for the lying in state because they felt “that need to come down”.
Ms Partridge, who left home at 3am to make the journey, said: “Even though they said it was closed I felt that need to come down.
“If we’ve got here and then they turned away, then fine. I would have just felt I needed to come and then be told I couldn’t go.”
Mr Hopkins said: “There was a sense of perhaps best not travel, but just to make the journey and just to check it out, and you know, if it ended in disappointment, then so be it.”
Ms Partridge had brought a walking stick with a seat because of problems with her knee, but otherwise the pair brought nothing with them.
She told PA: “I think we thought that we’re going to get down here and we were going to be turned away.
“That was the back of our minds anyway.”
Shiv Pandian, 58, from Raynes Park, south-west London, said his 30 years working as a urologist for the NHS had prepared him for a long wait.
“There’s lots of places to eat and toilets and things; you’re used to working long hours at the NHS,” he told PA, laughing.
“The Queen has served us for 70 years. I’ve served along with her for 30 years. I’ve seen three jubilees of hers, and I want to say goodbye.”
He added: “I got out at Waterloo and followed the queue backwards, and then at one point I was guided here to Southwark Park. Then it said reassuringly, it’s 14 hours from the entrance here, so I’m hoping by midnight today I’ll have seen the Queen.”
Paula Priest, 53, from Wolverhampton, said she was happy to wait “as long as it takes” to reach Westminster Hall.
“We’re here for the duration now, definitely.”
Those who braved the trip despite Government warnings were pleasantly surprised by the pace of the queue.
Later on Saturday morning the tracker had stopped telling mourners not to travel, and the wait had dropped to 16 hours.
There was constant movement through Southwark Park until the Thames path along Bermondsey Wall East where the queue became more stationary.
Bright pink wristbands, which state they do not guarantee entry to Westminster Hall, continue to be handed out.
Those waiting described the experience as well-organised, with friendly staff and officers on hand to assist.
The accessible queue resumed at midday, but around four-and-a-half hours later DCMS announced it had reached full capacity and is now permanently closed.
The department said wristbands for all time slots had been allocated for as many people as possible to pay their respects.
A DCMS tweet advised: “Please do not join the queue at Tate Britain. Thank you for your understanding.”