Miles Frost collapsed while out jogging at the family’s home in Oxfordshire on Sunday.
Friends said the financial investor had appeared “in wonderful form” in recent weeks and there was no indication of any health problems.
Sir David himself died two years ago aged 74 after suffering a heart attack on the Queen Elizabeth cruise ship.
Lord Chadlington, a long-standing friend of the Frost family, said: “It is very sad and very, very sudden. His family are very much in shock, but they are coping fine.”
He described Mr Frost as a “healthy man” rather than a fitness fanatic, saying: “He didn’t drink alcohol. He clearly led a life where he wanted to be as fit as he reasonably could be, and he liked having a few challenges.
“I had breakfast with him on Thursday and we spent the best part of two hours together. He was in wonderful form and it is a great shock to his family and friends.
“I am an investor in some of the companies he was involved in and we were planning what we were going to do in October and November. We were looking forward together and there was no hint of anything amiss.”
Lord Chadlington said the family are now “hunkering down” together as they come to terms with their grief.
“They are a very close family, very much a loving family, and they will sustain each other through this as they have other problems,” he said.
Mr Frost had two younger brothers, Wilfred, 29, a TV presenter on CNBC’s Worldwide Exchange programme, and George, 28, and all attended Eton.
Mr Frost was a financier and managing partner at Frost Brooks, a London-based private equity group.
Before founding the company, he spent five years at another private equity firm, LDC, working on technology, media and telecoms investments.
His company website says that his personal network “includes some of the most respected names in business and media”, many of whom have invested with Frost Brooks.
He was also a board member of Paradine Productions, Sir David’s TV production company; BizEquity, which enables business owners to gain an online value of their company; and parcel delivery firm Parcel Monkey.
Last year Mr Frost, his brothers and their mother, Lady Carina Fitzalan-Howard, were joined by 2,000 guests, including the Prince of Wales, for a memorial service at Westminster Abbey in Sir David’s memory.
Sir David was a television star for more than 50 years and was known for his incisive interviews - most famously with disgraced US president Richard Nixon.
Chris Hurley, chief executive of LDC, where Mr Frost worked between 2006 and 2010, said: “Miles was a charming and competent professional who was extremely popular with his colleagues.
“We’re all deeply saddened by the news. Our thoughts are with his family and friends.”