Few people stole a glance at the bespectacled former prison inmate, or were aware that he was living proof of a growing phenomenon.
The number of rough sleepers on London's streets has soared 43 percent over the past year, with Burn but one of many victims of Britain's continuing economic stagnation.
"If you haven't got a place, you look like a mess and so can't get a job, and if you haven't got a job, you've got to disgrace yourself on the street doing what I'm doing," Burn said.
The financial crisis has tested the reduced budgets of Britain's local authorities and charities, and seen a reversal of much of the progress made over the past decade.
Almost 6,000 people slept rough in London at some point during 2011/12, up from about 3,900 the year before, and 3,000 in 2006/7, according to statistics compiled by outreach groups and local authorities.
Of those 6,000, 62 percent were new to the streets.
Cheryl is one of them.
Crouched in a storefront near historic Trafalgar Square, she has slept rough since her father died three months ago and has developed a drug habit that saw her nearly overdose a few days previously.
"People just walk past us like we're not here. I sleep on the street and they wonder why I've turned to drugs."
"Hard isn't even the word for it," she said.
London still shapes up well, though, when compared to cities of similar size and stature.
Ten times more people sleep on New York's streets than on London's, government minister Grant Shapps told parliament earlier this year.
But colourful London Mayor Boris Johnson had pledged to eradicate rough sleeping by 2012, while the city's hosting of the Olympics over the Summer had seen it take further steps to accommodate its homeless.
Now the Conservative-led coalition government has introduced additional cuts to housing benefits that some charities say will aggravate the situation.
"The coalition is sweeping away the safety nets that have traditionally saved people from the horrors of homelessness," said Leslie Morphy, chief executive of the charity Crisis.
Amidst comprehensive cuts in almost every area of state spending, the government says it is doing its best to confront the problem.
"As a government, we are determined to engage with this issue, and ensure the right intervention is made as early as possible," said Housing Minister Mark Prisk at the launch of a rough-sleeping hotline earlier this month.
"We need to break the habit to help people turn their lives around," he added.
London authorities too say they are doing all they can, and have set up a "No Second Night Out" scheme to try and root out and shelter new rough sleepers.
But for those too seasoned to the streets to qualify for such programmes, Christmas is a particularly bleak time of year.
"The hostels are all full up because it's so cold. Sometimes people are more generous, but it's an expensive time of year for them as well," said Nick, a softly spoken, tattooed man sitting cross-legged with his dog opposite the opulent Savoy Hotel.
He says he ended up on the street eight years ago when he split with his wife and his life unravelled.
Single men, who stand at the bottom of the public housing pecking order, are particularly liable to end up on the streets.
The fear is, however, that those reduced to sleeping in the freezing conditions are merely the most visible casualties of Britain's grave housing shortage.
The number of people sofa-surfing or living in overcrowded housing - hidden homelessness - has also soared, according to research by Heriot-Watt and York universities.
The government says it supports the building of up to three million new homes by 2020 to house Britain's growing population.
In London, where private rents have rocketed and public housing has struggled to keep pace with an influx of foreign and domestic migrants, help cannot come soon enough.
For some already sleeping on the streets, it might be all too little too late.
"I've become street-institutionalised," said a man known as Billy-militant because of his habit of railing against the government.
"I'm used to it. I don't know anything else."
(Editing by Stephen Addison)