His court martial for refusing to return to Afghanistan is due to be held next month. At the moment he is confined to barracks on weekdays.
Defending his appearance at the demonstration, he said: "This is my choice.
"Somewhere down the line it's all going to come apart and people are going to be prosecuted for these things."
'It's scary stuff'
L/Cpl Glenton said people who believed he had brought disgrace upon the British Army were "entitled to their opinion".
He said: "I think what I am doing is in the British interest. I take my duty very seriously."
The soldier could be sent to prison for going absent without leave in 2007, something he said he was not looking forward to.
He said: "It's scary stuff, I have a wife and a family.
L/Cpl Joe Glenton (right) led the march from Hyde Park
"I don't want to [go to prison] but if I gone back [to Afghanistan] and been involved in that and caused the deaths of innocent people then I would never be able to shrug that off, I would never had been free.
"The fact that I said no is fairly liberating, I can assure you."
Another speaker in Trafalgar Square was Peter Brierley whose son, L/Cpl Shaun Brierley, was killed in Kuwait in 2003.
Mr Brierley, from Batley in West Yorkshire, confronted former Prime Minister Tony Blair at a memorial service at London's St Paul's Cathedral, telling him: "You have my son's blood on your hands."
Speaking at the demonstration, he said: "They [the military] are not doing any good while they are over there.
"They need to leave the country to sort itself out. While the British troops are there they are actually bringing in insurgents who are coming in to fight."
'Key to security'
Meanwhile, a survey suggests that public support for the war has fallen further. The YouGov survey for Channel 4 News found that 62% of those questioned wanted British troops withdrawn in the coming year at the latest.
Of 2,042 adults polled, 6% said that British troops were winning the war, compared with 36% who said they were not winning yet but eventual victory was possible, and 48% who said that victory was not possible.
A similar survey in 2007 found that 36% thought that victory was impossible.
A spokesman for the MoD said on Friday: "It is vital to the UK that Afghanistan becomes a stable and secure state that is able to suppress violent extremism within its borders.
"Britain's own security is at risk if we again allow Afghanistan to become a safe haven for terrorists, and that would be the result if Nato forces were to pull out of the country immediately."
In February 2003, an estimated one million took part in a march in London against the Iraq war.
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