International leaders, royalty and families of the fallen have united in the UK and in Belgium to mark 100 years since Britain entered the first world war.

The day of commemorations culminates with lights across Britain being turned off between 10pm and 11pm, at which time a single candle at Westminster Abbey will be doused to mark the exact moment a century ago that the country declared war on Germany. The ritual is to evoke the famous observation of the then foreign secretary, Edward Grey: "The lamps are going out all over Europe".

Flowers are placed around the Grave of the Unknown Warrior before a candlelight vigil for the first world war at Westminster Abbey in London. Photograph: Dan Kitwood/Getty Images

It is a day of reconciliation, silent reflection, candlelit vigils, wreath-laying, gun salutes and the strains of the Last Post as countless ceremonies are held.

In the UK, dignitaries from across the Commonwealth gathered in Glasgow Cathedral at 10am, including the Prince of Wales, the prime minister, David Cameron, and Scotland's first minister, Alex Salmond, to join a congregation of 1,100.

The broadcaster Sir Trevor McDonald reminded them of the human cost paid by Britain – 6,146,000 men serving, 761,000 killed, 1,600,000 wounded – as well as 206,000 Irishmen, of whom 30,000 died.

Prince Charles and David Cameron leave Glasgow Cathedral after the service to mark the centenary of the first world war. Photograph: Jeff J Mitchell/Getty Images

A procession of children carried candles candle down the cathedral's aisle to symbolise the "candle of peace and hope" passing to the new generation. Afterwards, at the Cenotaph in Glasgow's St George's Square, poppy wreaths were laid.

As he entered the cathedral, where a silk poppy was placed on every seat, Cameron spoke of how the first world war had "profoundly changed our world". Nearly every family, and every community was affected, he said. "Almost a million British people were lost in this war, it's right that almost 100 years on we commemorate it, we think about it, and we mark it properly."

But, along with the terrible loss of life and suffering, the war also changed the world for better, he said. "The emancipation of women, the fact that women then got the vote, participated more in the workplace; there were changes in medicine, massive improvements in our world – all those things are worth remembering and that's why, as a government and as a country, we should be refurbishing our war memorials, and we are," he said.

In Belgium, whose invasion by Germany lit the touchpaper that plunged Europe into four years of darkness and the most destructive warfare the world has seen, government leaders and royalty gathered in Liege. Reduced to rubble, the city was awarded the prestigious French Legion d'Honneur.

At the Allies' War Memorial of Cointe, overlooking the city, former enemies were united as the Duke and Duchess of Cambridge joined Belgium's King Philippe and Queen Mathilde and the French president, François Hollande, to welcome the German president, Joachim Gauk.

The Duke and Duchess of Cambridge sit with French president François Hollande at the first world war ceremony at the Allies' Memorial in Cointe, Belgium. Photograph: Splash News/Corbis

Belgium had been the first battleground of the war, said Hollande, offering "solid resistance" in Liege, with "deadly days" to follow.

Cannon were fired before Philippe laid wreaths at the foot of the memorial. Paying tribute to the "courage and dignity" of those fighting , the "cruelty and barbarism" of the war, he spoke too of the challenge of keeping peace. "Peaceful Europe, unified Europe, democratic Europe. Peace is what our grandparents longed for".

Gauck said Germany's invasion of neutral Belgium, was "unjustifiable". "We are grateful to have been able to live together with peace for so long in Europe", he said.

Prince William, representing the Queen, praised Belgium and its people "whose resistance was as gallant as their suffering was great" and spoke of the power of reconciliation. .

"We were enemies more than once in the last century, and today we are friends and allies," he said. "We salute those who died to give us our freedom. We will remember them."

During the ceremony a girl, symbolising the passing on of remembrance for future generations, released a white balloon as a sign of peace and reconciliation, along with thousands of other balloons in the colours of the flags of other countries invited to the commemoration.

Belgium's King Philippe watches a girl release a white 'peace' balloon at a first world war ceremony in Liege. Photograph: Bruno Fahy/AFP/Getty Images

Later on Monday the duke and duchess of Cambridge will join 500 guests, including Cameron and Prince Harry, at a twilight ceremony at St Symphorien military cemetery in nearby Mons, where 229 Commonwealth and 284 German troops are laid to rest, including the first and last British soldiers to die on the western front.

Before leaving for Belgium, Harry was in Folkestone for the unveiling of a memorial arch on the Road of Remembrance, which many troops walked on the way to embarkment, and which for so many was the last sight of home.

British commemorations will culminate at Westminster Abbey, when the flame of a single oil lamp at the tomb of The Unknown Warrior will be extinguished at 11pm – the exact moment of the declaration of war. It will be the finale of a candlelit vigil at the abbey, one of many being held at churches and war memorials throughout the country, including at St Anne's Cathedral in Belfast, and Llandaff Cathedral, Cardiff.

During the vigil, to be broadcast on BBC2, more than 1,000 candles held by the congregation will be slowly extinguished. The candle on the tomb, which has been a powerful focus of prayers for peace since the unknown soldier was moved from a battlefield cemetery in northern France on Armistice Day in 1920, will be put out last by the Duchess of Cornwall, representing the Queen, who is marking the anniversary at Craithie Kirk, near Balmoral.

Red ceramic poppies fill the Tower of London moat to commemorate the fallen of the first world war in Paul Cummins' art installation, Blood Swept Lands and Seas of Red. Photograph: Paul Brown/Rex

The Paschal Candle alone will remain alight, as all over Britain lights will be turned off in homes, offices and public buildings, with each leaving on just a single light or candle.

The abbey service will feature 1914 poetry readings, the author and broadcaster Sebastian Faulks reading from his novel Birdsong, and the performance of Ralph Vaughan Williams' The Lark Ascending, written in 1914.

The Dean of Westminster, the Very Rev Dr John Hall, said: "This vigil will bring into focus our national remembrance of the centenary of the first world war … As together, in the abbey, in cathedral and churches across the nation and through the media of television, we reflect on the impact of the beginning of the war, may we collectively resolve to continue to strive for peace, justice and freedom throughout the world."