Thousands of veterans marched past the Cenotaph in London on Remembrance Sunday as Britain paid its respects to the fallen of past conflicts.

The Queen led commemorations at the memorial to “The Glorious Dead” in Whitehall, while services were held at churches, war memorials and cemeteries across the country.

The prime minister, Boris Johnson, and Labour’s Jeremy Corbyn joined other party leaders in laying wreaths on the 100th anniversary of the first Remembrance Day in 1919.

They stood with heads bowed as Big Ben struck 11am, and a two-minutes’ silence was marked by the firing of a gun by the King’s Troop, Royal Horse Artillery and a bugler’s Last Post.

The Prince of Wales laid a wreath on behalf of the Queen, who watched the ceremony from a balcony overlooking the memorial first unveiled by George V in 1919.

After the service, a large crowd cheered as veterans, and others involved in armed service personnel organisations and charities, performed the traditional march past. Some used wheelchairs, mobility scooters or walking sticks and were well into their tenth decade. But, medals glinting in the autumnal sunshine, they passed the Cenotaph and saluted, eyes left.

Ron Freer, 104, from Kent, was thought to be the oldest veteran taking part in the march past. Before the ceremony, he said he felt “hugely honoured” and planned to march alongside 100 other blind veterans.

The Taxi Charity for Military Veterans said London cabbies had made more than 1,000 free taxi journeys as part of the Poppy Cabs initiative, which helps with veterans travel in the capital funded by the drivers themselves.

Five former prime ministers – Sir John Major, Tony Blair, Gordon Brown, David Cameron and Theresa May – were among those paying tribute. They joined senior military leaders, faith community leaders and representatives of other Commonwealth nations.

The Duke of Edinburgh, 98, a second world war veteran who served with the navy and was mentioned in dispatches for his part in the Battle of Cape Matapan, was not present. He retired from official royal engagements two years ago.

The dukes of Cambridge and Sussex laid their own wreaths as their wives watched from nearby balconies along with other members of the royal family. The march-past salute was taken by the Duke of York, who was accompanied by the defence secretary, Ben Wallace.

For the first time, the ambassador of Nepal placed a wreath in honour of the contribution the Gurkha regiments made to Britain’s military campaigns. Wreaths were also laid for the the first on behalf of the intelligence services, to coincide with the 100th anniversary of GCHQ and the 110th anniversaries of MI5 and MI6.

As the nation fell silent to remember the fallen, a second world war Dakota plane released 750,000 poppies over the white cliffs of Dover, as hundreds of people packed the nearby Battle of Britain memorial. The former US military transport plane was flanked by two Spitfires as it flew low over the Kent coast to release the biodegradable poppies.

WO Roy Briggs, 94, one of five RAF veterans on board, said he spent the flight thinking of a Lancaster crew he knew who lost their lives during a mission. “I am 94, and they are still 20 and 21. They will never be anything else to me,”he said.

In Edinburgh, the first minister, Nicola Sturgeon, attended the official wreath-laying ceremony at the Stone of Remembrance.

In Enniskillen, where 12 people were killed and 68 injured at the Remembrance Sunday IRA Poppy Day bomb attack in 1987, the Irish prime minister, Leo Varadkar, was among dignitaries from both side of the Irish border to lay a wreath.

This year marks the 75th anniversary of D-Day, the Battle of Kohima in India, the Battle of Arnhem in the Netherlands and the Battle of Monte Cassino in Italy.

Boris Johnson tweeted he would be thinking of those over the centuries who had given so much to protect the country. “I will especially remember the men and women who gave the ultimate sacrifice in war, so that today we can live in peace.”

Corbyn paid tribute to the work of the armed forces in a video tweeted before the ceremony. In it he said: “We remember the many brave people from Britain and all across the world who put their lives on the line making huge sacrifices in two world wars which cost the lives of millions, and in all other conflicts since. And we stand together to say: ‘Never again.’”

A campaign to ensure Remembrance Sunday can be celebrated by everyone “irrespective of nationality, creed or colour” has been backed by MPs, the faith community and former military leaders. Coordinated by the Royal British Legion and the British Future thinktank, Remember Together encourages people from different background to commemorate their shared history 75 years after major battles of 1944.