Tributes have flooded in on social media after Mr Fingleton, who played the giant Mag the Mighty in the fourth season of the HBO series, reportedly died of heart failure on Saturday.
Mr Fingleton, who at 7ft 7in was once declared Britain's tallest man, also portrayed villain The Fisher King in Doctor Who.
He also had a role 2011 film X-Men: First Class.
Game of Thrones star Ian Whyte, who also played a giant on the show, tweeted: "Very sad to hear of the tragic passing of Neil Fingleton. He followed his dreams. Rest in peace."
Mr Fingleton grew up in County Durham but moved to the US to build a career in basketball, before he turned his attention towards acting.
He was declared the UK's tallest man in 2007.
His most famous acting role came in 2014, when he appeared as Mag Mar Tun Doh Weg, or Mag the Mighty.
Mr Fingleton gave an interview to the Journal in 2007 after being crowned Britain's tallest man, and said he was used to getting attention because of his oversized stature, reports the Newcastle Chronicle.
He said: “I do cause a bit of a stir wherever I go, with people pulling out cameras, but it doesn’t bother me. I’ve never been embarrassed about my height and I actually like the size I am. It’s something unique and original.
My group of friends are great and I come from a good family, so being tall hasn’t ever been an issue. I’ve not been self-conscious.”
The Tall Persons Club, an organisation which works with extremely tall people, posted on Facebook: “Sadly it has come to our attention that Neil Fingleton, Britain’s Tallest man passed away on Saturday. Our thoughts and condolences go out to his family.”
Back in 2008, speaking about his acting career, Neil said: "My height has given me a way into the entertainment industry, which is where I want to be. I’ve been offered a TV show in the States called My Giant Life so I’m just waiting for my visa.
I won’t do anything degrading. I have been asked to do porn before but I’ve always refused. I’d find it dehumanising and exploitative.
I don’t mind having a bit of fun with my height. But when it’s fun at my expense then I’ll draw the line.
I’m proud to be tall. I’ve always had good friends around me and it’s never been something they’ve frowned upon.
I never experienced any bullying at school and my parents always taught me to appreciate my uniqueness.”
