A Foreign Office spokesperson said: “We are supporting the family of a British national who has died in Thailand and are in contact with the local authorities.”
Police in Pattaya told the BBC Griffiths was found dead outside a luxury hotel where he had been staying in as a long-term resident in a suite on the 17th floor.
He was involved in two ongoing court cases that might have caused him stress, police also told the BBC.
Griffiths was separated from his second wife, a Thai national, and had reportedly been engaged in a legal dispute with her over a business they ran together, the BBC understands.
He co-founded Asos in London with Nick Robertson, Andrew Regan and Deborah Thorpe.
Its name originally stood for As Seen On Screen as it sold fashion inspired by clothing worn by TV and film stars.
It grew to become an online fashion marketplace stocking hundreds of brands as well as its own lines and at one time was valued at more than £6bn.
Its largest shareholders include Danish billionaire Anders Holch Povlsen – who owns Danish clothing giant Bestseller and Mike Ashley, owner of Frasers Group.