Hamit Coskun, 51, shouted abusive comments about Islam as he held the flaming book aloft in Rutland Gardens, Knightsbridge, on February 13.
In June, he was found guilty at Westminster Magistrates' Court of a religiously aggravated public order offence and fined £240.
At Southwark Crown Court on Friday, Justice Bennathan said that while burning a Quran might be something "many Muslims find desperately upsetting and offensive", the “right to freedom of expression must include the right to express views that offend, shock or disturb".
The judge added: "We live in a liberal democracy. One of the precious rights that affords us is to express our own views and read, hear and consider ideas without the state intervening to stop us doing so.
"The price we pay for that is having to allow others to exercise the same rights, even if that upsets, offends or shocks us."
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Blasphemy laws were abolished in England and Wales in 2008 and in Scotland in 2021.
Source: Agencies