Cardinal Murphy-O'Connor, who became leader of the Roman Catholic Church in England and Wales in March 2000 before retiring from his role in 2009, died on 1st September at the age of 85 having suffered from cancer.
Conservative MP Jacob Rees-Mogg joined former Irish president Mary McAleese at Westminster Cathedral.
His death prompted tributes from Pope Francis and former prime minister Tony Blair.
Around 1,200 mourners filed in to the cathedral, for the ticket-only mass.
Dozens of bishops and more than 300 priests from across the church followed, filling the seats at the front of the cathedral, where the late cardinal's coffin rested before the altar.
Representatives of other Christian churches including the Archbishop of Canterbury Justin Welby, and his predecessor Dr Rowan Williams, Baron Williams of Oystermouth, took part in a procession down the aisle as the mass began.
Adam Simon who attended the funeral and considered himself a friend of Cardinal Cormac told Premier it was "a very reverential occasion".
He told Premier what he's lasting memory of the Church leader is.
"He was beacon of light, a father like figure, a rock to us all," he said.
"I have a photo of Cardinal Cormac he was blessing our children but he was blowing bubbles with them... that was the type of person that he was. He was a holy man but he was a human person and he was a friend to the family and to so many people."
Addressing the congregation Cardinal Murphy-O'Connor's nephew paid tribute to his devotion to family.
Patrick Murphy-O'Connor, who said there were around 95 relatives at the funeral, added: "Cormac was much-loved and he would do anything for his family."
The cardinal was "a priest to his fingertips" and "supremely confident in his calling", Archbishop of Cardiff George Stack said as he gave a homily.
He said: "He was a gifted man who would have made a success of whatever career he chose."
But he learned "a huge lesson", the archbishop said, in an apparent reference to a controversy faced by Cardinal Murphy-O'Connor around how the church handled claims of child sex abuse.
The cardinal, while Bishop of Arundel and Brighton, decided to move Father Michael Hill to the chaplaincy at Gatwick Airport in 1985 when he was warned that the priest was a threat to children.
Hill was jailed in 2002 after pleading guilty to indecent assault against three boys, including the abuse of a teenager with learning difficulties who went to the airport's chapel after missing a flight.
Explaining the appointment to Gatwick Airport, the cardinal said he had received "conflicting psychiatric reports" and believed Hill would not have access to children.
He apologised on several occasions to Hill's victims, saying he had made a "grave mistake" and that he had been "naive and ignorant" in his handling of allegations of sex abuse involving Roman Catholic priests.
Archbishop Stack told mourners: "He acknowledged his mistakes. He made no excuses. He said the most difficult words of all, 'I'm sorry'.
"He learned a huge lesson and proceeded to establish the most robust safeguarding mechanism possible, a model for other institutions.
"Humility and action were part of the robe that he wore."
The Nolan report, commissioned by the cardinal in 2001 and drawn up by the retired Roman Catholic law lord, led to a stringent set of guidelines to prevent child abuse in the Catholic Church in England and Wales.
Following the the mass, which was taken by the current Archbishop of Westminster Cardinal Vincent Nichols, Cardinal Murphy-O'Connor was buried within a vault in the cathedral below the 10th station of the cross.
