Gilmour, the stepson of Pink Floyd guitarist Dave Gilmour, wrote in a newspaper that he had been told by police and probation officials to stay away from the capital because he "poses too much of a threat".
The 21-year-old was given a 16-month jail sentence last year after swinging from a flag on the Cenotaph while high on LSD, Valium and whisky when student protests turned to riots in December 2010. He was released eight months ago.
Gilmour wrote in the Mail on Sunday: "It's lucky I gave up my childhood dream of high-jumping for Britain because I am banned from staying in London during the Games.
"The Metropolitan Police and the probation service decided I pose too much of a threat, which shows how much faith they have in the rehabilitative powers of the British penal system."
Police and probation officials are understood to have varied the conditions of Gilmour's release to introduce the ban on staying in the capital.
In his article, Gilmour railed against the Olympics, claiming that following last summer's riots, the vast sums being spent on the Games could become a fresh "source of rage".
He wrote: "Last summer's riots were disgraceful. But it is my belief that Cameron's and Clegg's cuts have looted the prospects of the young who, for the first time in British history, can expect to be worse off than their parents.
"The billions the Government is throwing at the Olympics can only be a source of rage when, at the same time, the most vulnerable members of society are having the floor ripped from beneath them.
"At every turn the Government is sending out one message loud and clear to the young and increasingly dispossessed, and that is, 'We don't care'."
During the student riots in 2010, Gilmour was part of a mob that ransacked a clothes shop and attacked a convoy that was carrying the Prince of Wales and the Duchess of Cornwall.
He was freed four months into his sentence and returned to Girton College, Cambridge to complete his history degree.