Clemens, honoured by The Queen in 2010 for services to broadcasting and drama, died on Saturday, his family confirmed.
One of his sons, George Clemens, said:
He was a true inspiration.
He told the BBC:
The world has lost a really great man who has given so much.
Born in Croydon in 1931, Clemens had his first work commissioned by the BBC in 1955.
He went on to be a staff writer for a film and TV production company, before enjoying considerable success with a huge number of TV scripts in the 1960s.