The pope yesterday apologised for the "unspeakable crimes" committed by Catholic priests who sexually abused children.

In the most strongly worded public apology of his state visit to the UK so far, the pontiff spoke of the "shame and humiliation" brought by the scandal.

He told the congregation at London's Westminster Cathedral: "I think of the immense suffering caused by the abuse of children, especially within the church and by her ministers.

"Above all, I express my deep sorrow to the innocent victims of these unspeakable crimes, along with my hope that the power of Christ's grace, his sacrifice of reconciliation, will bring deep healing and peace to their lives.

"I also acknowledge with you the shame and humiliation which all of us have suffered because of these sins."

Yesterday's sermon was delivered in front of a congregation including former British prime minister Tony Blair and his wife Cherie.

Focusing on those who suffered at the hands of clergy, he added: "I invite you to offer it to the Lord with trust that this chastisement will contribute to the healing of the victims, the purification of the Church and the renewal of her age-old commitment to the education and care of young people.

"I express my gratitude for the efforts being made to address this problem responsibly, and I ask all of you to show your concern for the victims and solidarity with your priests."

His comments follow his strongest admission to date of failings in the way the abuse scandal was handled.

On his flight into Britain, he said the Catholic church had not dealt with abusive priests decisively or quickly enough and said its top priority now was helping victims heal and regain their trust in the Church.

Earlier yesterday morning the pontiff was greeted by Prime Minister David Cameron – the first time the two men have met since the pope arrived in the UK.

The pope also spoke with other political figures including deputy prime minister Nick Clegg and acting opposition leader Harriet Harman.

The pope addressed the crowd outside Westminster Cathedral, urging them to "make space for silence" amid the stress of daily life.

About 2,000 youths from dioceses in England, Scotland and Wales were gathered in the piazza, while thousands more worshippers were packed on the road beyond.

The pope said: "I ask each of you, first and foremost, to look into your own heart. Think of all the love that your heart was made to receive, and all the love it is meant to give. After all, we were made for love." He said while at times "our hearts brim over with generosity", at other times "our hearts can easily be hardened by selfishness, envy and pride".

He continued: "Even amid the 'busy-ness' and the stress of our daily lives, we need to make space for silence, because it is in silence that we find God, and in silence that we discover our true self."

He also spoke of his sadness at being unable to visit Wales during his trip to Britain.

In an address to the people of Wales, broadcast from a mass at Westminster Cathedral in London, the pope blessed the nation in Welsh and said he was happy to honour its people and its ancient Christian tradition.

He highlighted the sixth-century St David, the patron saint of Wales. "David's preaching was simple yet profound – his dying words to his monks were 'be joyful, keep the faith and do the little things'."

He added: "May St David's message, in all its simplicity and richness, continue to resound in Wales today, drawing the hearts of its people to renewed love for Christ and his church."

The pope was speaking after he blessed a new mosaic of St David installed in Westminster Cathedral earlier this month.

He also prayed before the statue of Our Lady of the Taper, the Welsh national shrine to Our Lady, brought from Cardigan in Wales to mark the occasion.

The pope said he hoped the statue, set to return to Cardigan, would be a "lasting reminder" of his "deep love" for the Welsh people.

He concluded his address: "Bendith Duw ar bobol Cymru. God bless the people of Wales."