After six days of heartbreaking testimony by bereaved families at the new inquest into how 96 people met their deaths at the Hillsborough football ground in 1989, there was a warmth close to celebration to the service at Liverpool's sun-blessed Anfield home marking 25 years since the disaster.

The grievous loss the families suffered was remembered: of sons, daughters, fathers, grandfathers, fathers-to-be, a mother – who went off to support Liverpool in that FA Cup semi-final against Nottingham Forest under similar spring sunshine and clear blue skies.

But the speeches by Trevor Hicks, both of whose daughters, Sarah, 19, and Victoria, 15, were killed in the crush, Margaret Aspinall, who lost her 18-year-old son James; the Liverpool and Everton football managers Brendan Rodgers and Roberto Martínez, and the Labour MP Andy Burnham, dwelled more on the other, remarkably life-affirming side of the Hillsborough story: the families' relentless fight for justice.

It was the word spoken more than any other on this day of solidarity, emblazoned on many scarves raised above heads among 24,000 people in the ground: justice, for the 96. Hicks recounted the families' long campaign against the original 1990-91 inquest, the quest for the truth about what really caused the crush on the Leppings Lane terraces, and for accountability.

It was a campaign without result until five years ago when Burnham's address as a Labour minister to the 20th anniversary service was drowned out by the crowd's call for justice. That led to Burnham's initiative to have all official documents relating to the disaster published, then the landmark September 2012 Hillsborough Independent Panel report, followed three months later by the high court quashing the inquest, after 21 years.

This time, in an age of expenses scandals and seemingly ubiquitous mistrust of politicians, Burnham – widely recognised to have overturned years of official inaction and helped deliver a justice process – was welcomed with an immediate standing ovation. He took as his theme the families' determination, the togetherness of Liverpool and its two rival football clubs, as displayed by Martínez paying his respects in the home of his club's fiercest sporting rival.

"Your voices were carried off the Kop and into the heart of the establishment," Burnham said of the justice calls in 2009. "That was the moment the dam burst, and asked the most profound questions about our country, and how it is run. How could a whole city be crying injustice, and nobody was listening? In time, your fight will make our country fairer."

Describing the "dignity, courage, humanity" of the families, who were sitting quietly in rows in front of him, he told them: "You are truly the best of us."

That tribute was echoed by Rodgers, who mentioned some of Liverpool's great players, its iconic manager Bill Shankly, and his own predecessor Kenny Dalglish, who as the manager in 1989 identified intensely with the families and personally attended many of the funerals.

"But without doubt the single biggest source of inspiration is every morning at Anfield, seeing the Hillsborough memorial, the 96 names," said Rodgers, who has led his team to becoming favourites to win this season's Premier League, with four games to play. "You who have fought so long on their behalf, and on behalf of the survivors, you are the true inspiration."

The priests of three local churches read out the names of those who died, and a candle was lit for each name. This part of the service took more than eight minutes, to a crowd which had fallen completely silent.

Now, after the opening of the new inquest which is featuring the families' personal statements about the victims, the world finally knows more about them, hearing of rounded, beloved, hardworking, talented people whose futures were lost, not just names on the long memorial list outside Anfield's Shankly gates.

John Anderson, alphabetically the first, was remembered at the inquest by his son Brian, who was also at Hillsborough and survived the crush. He said his 62-year-old father was a fit amateur referee, married for 42 years, whose family were robbed of his retirement.

Six days of family testimony have covered 45 of those who died, not yet half; other families have gasped and wept hearing detail for the first time. One victim discussed on the first day was Patrick Thompson, who was killed at 35 leaving five children all under six.

"Please listen to the evidence, and let my children know that their dad was not a hooligan, but a hardworking man who just happened to love football," his widow Kathleen had asked the jury, referring to the accusations of drunkenness made against the Liverpool fans by South Yorkshire police after the disaster.

Peter Thompson, not related to Patrick, was married and his wife was expecting their baby, when he went to the 1989 FA Cup semi-final and never came home. His daughter, Nikki, was born four months after he died.

When the candle was lit for Alan McGlone, 28 when he went off to the match, the crowd could recognise him as the father whose widow Irene told the inquest how their two infant daughters, Amy, then five, and Claire, then two, had asked her to send him in to wake them up when he came back.

"I am still waiting to wake my girls up from this nightmare," Irene said in her statement.

After a break for the memorial service and Easter, the families are back in Warrington, Cheshire, to hear evidence about the 51 other victims. The new inquest is scheduled to last a year.

This service celebrated the families' enduring love above all else, and culminated in Gerry Marsden singing You'll Never Walk Alone, his original hit, long since adopted as the anthem of Anfield. The qualities of the Hillsborough families were recognised here, for having held their heads up high, and not walking alone through their storm.