Sir Donald read Meditation 17 from 17th Century poet John Donne's Devotions Upon Emergent Occasions.
Sir Alec Guinness, Sir Donald Sinden and Sir John Mills joined Dame Maggie Smith and Lord Attenborough at a service near Sir John's home in Buckinghamshire on Thursday afternoon.
Sir John was later cremated in Oxford.
Actresses Irene Worth and Nanette Newman, and Anthony Andrews - with whom Sir John starred in Brideshead Revisited - were also at the service and cremation.
His nephew, Adam, and niece, Maina, were also present.
Leading the tributes at the service in the parish church of Wotton Underwood, near Aylesbury, was actor Paul Scofield, who read Shakespeare's Sonnet No 71.
Sir Donald read Meditation 17 from 17th Century poet John Donne's Devotions
Upon Emergent Occasions.
Other readings included Corinthians Chapter 13.
The service also included a rendition of Jesu, Joy of Man's Desiring.
Speaking after the cremation, solicitor Ian Bradshaw, one of the executors of Sir John's will, said: "It was a very simple and moving ceremony, in accordance with Sir John's wishes - a simple ceremony with no hymns and no mourning."
One of the greatest performers of his generation, Sir John died at his home on Sunday 21 May, aged 96.
He was the last of a generation of classical actors, including Laurence Olivier, Ralph Richardson and Peggy Ashcroft, who dominated British theatre from the 1930s to the 1970s.