Dr Richard Chartres noted the conflicting opinions on Lady Thatcher's legacy but said today was "neither the time nor the place" to debate this.
"After the storm of a life lived in the heat of political controversy, there is a great calm," he told the more than 2,000 guests at St Paul's Cathedral.
"Lying here, she is one of us, subject to the common destiny of all human beings.
"There is an important place for debating policies and legacy ... [but] this is a place for ordinary human compassion of the kind that is reconciling. It is also the place for the simple truths which transcend political debate. Above all it is the place for hope," he said.
Lady Thatcher had been involved in the planning of her funeral for some years. She requested that there be no eulogies and that the serving Prime Minister, regardless of party, give a reading.
David Cameron read from John 14.1-6, a passage requested by Thatcher:
Let not your heart be troubled: ye believe in God, believe also in me.
In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you.
And if I go and prepare a place for you, I will come again and receive you unto myself; that where I am, there ye may be also.
And whither I go ye know, and the way ye know. Thomas saith unto him, Lord, we know not whither thou goest; and how can we know the way? Jesus saith unto him, I am the way, the truth and the life: no man cometh unto the Father, but by me.
Although the mood was sombre, the bishop drew smiles and laughter as he recalled sitting beside Lady Thatcher at a City function and being told by her: "Don't touch the duck paté, Bishop - it's very fattening."
He also reflected on her Christian faith, which she often spoke of during her political career.
The congregation heard a quote from a lecture she gave in the nearby church of St Lawrence Jewry in which she said: "We often went to church twice on Sundays, as well as on other occasions during the week… We were taught always to make up our own minds and never take the easy way of following the crowd."
The bishop said the country "owes a huge debt" to the Methodism in which she was raised.
"When it was time to challenge the political and economic status quo in nineteenth century Britain, it was so often the Methodists who took the lead," he said.
He went on to comment that her oft quoted remark, that there was "no such thing as society", was "misunderstood" and "refers to some impersonal entity to which we are tempted to surrender our independence".
He concluded with another comment on hope: "The natural cycle leads inevitably to decay, but the dominant note of a Christian funeral service, after the sorrow and the memories, is hope."
Prayers were offered during the service by Catholic and Methodist leaders.
The blessing was given by the Archbishop of Canterbury, to Most Reverend Justin Welby, who said: "Support us, O Lord, all the day long of this troublous life, until the shadows lengthen and the evening comes, the busy world is hushed, the fever of life is over and our work is done."
Thatcher's coffin was draped in a Union flag for the service. There were applauds and cheers from the large crowds who lined the streets of central London to see it taken in procession to the cathedral.