Three of the five are Cambridge graduates, and all three won their awards for roles in the BBC's The Night Manager.
Meanwhile The Crown - which follows the life of Queen Elizabeth II from her wedding day onwards - was named best drama series, with its star Claire Foy also picking up the prize for best drama actress.
The actor told the star-studded crowd: "Thank you first to the Hollywood Foreign Press Association for this awesome honour".
In the TV section, The Night Manager was the biggest victor.
The mini-series for which these actors were commended was itself written by Oxbridge graduates. The Night Manager, which the eponymous series was based on, was written by Oxford graduate John le Carré in 1993, and was adapted for screen by Cantab David Farr.
After applauding his costar, Tom Hiddleston extended his hand for a congratulatory shake, but he was a few seconds too late as Laurie had just turned his attention toward the award stage.
He dedicated his win to aid workers in South Sudan, where he had recently travelled, and where he said he had met humanitarian personnel who had watched the show while sheltering from shelling. Thanking the Hollywood Foreign Press Association for the award, the British actor quipped that he had won at the "last ever" Golden Globes, Mashable reports.
"Thank you, this is obviously a bad mix-up", he said upon accepting his award.
In a reference to US President-elect Donald Trump, he continued: "I don't mean to be gloomy".
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