Tens of thousands of Scottish independence supporters marched through Edinburgh on Saturday, as pressure built on the Scottish National party leadership to decide on the timing of a second referendum.

Organisers said more than 100,000 people took part in the march through the capital in what was hailed as the “biggest and boldest” demonstration for independence in Scotland’s history.

Gary J Kelly, from All Under One Banner, who organised the march, said the desire for constitutional change was proven by the sheer size of the turnout.

“The passion is there for definite at the end of the day,” he told the BBC. “The SNP asked us to speak; well, the people have spoken. We’ve done it all year round.”

The event came 24 hours before the beginning of the Scottish National party’s conference in Glasgow, and although there are no independence-related debates scheduled for the party conference, the party’s deputy leader, Keith Brown, was among those at the front of the rally as supporters demanded independence.

After the demonstrators arrived at Holyrood park, next to the national parliament, Brown and others addressed the crowd from a stage.

Linda Hamilton, from Glasgow, was among those who took part. She said: “I believe in Scottish independence, and I believe today is a demonstration – a visual demonstration – that there is a need for independence in our country.”

There were a small number of union-supporting counterprotesters on the Royal Mile as the pro-independence crowds walked past. Scotland in Union chief executive Pamela Nash said: “Poll after poll shows that a majority of Scots don’t want a divisive and unnecessary second independence referendum.”

Organisers lodged a formal complaint of bias with the Scottish government after Historic Environment Scotland refused to allow marchers to congregate at the park, saying it did not allow “political events of any nature” to take place on its properties.

March organisers claimed on Friday that the ban had been overturned, and HES said on Saturday that its priority was to facilitate the march safely after the public body had previously insisted it remained in force.

A demonstrator holds a hybrid saltire/EU flag. Photograph: Russell Cheyne/Reuters

Martin Keatings, the convenor of the pro-independence Forward as One, which lodged the complaint about HES, said the ban breached human rights and rights of access laws. He referred to a case in August, when an employment tribunal judge ruled that equality law protected support for Scottish independence because it was a “philosophical belief” similar to a religion.

The event marked the culmination of a summer of marches across the country organised by All Under One Banner, a non-aligned grassroots group. The first march through Glasgow in May attracted about 40,000 people, who held saltires and “Still Yes” placards during the largest public demonstration in the city since the rally against the Iraq war in 2003.

A pro-independence supporter at the march. Photograph: Russell Cheyne/Reuters

AUOB organisers have called for a second vote to be held before 2021, which marks the end of the Brexit transition period and the next Holyrood elections.

Those involved with the wider independence movement report a growing frustration among grassroots activists about a perceived lack of leadership from the SNP, in particular the way its leader, Nicola Sturgeon, appears to have tied the fate of the next referendum to Brexit. The first minister has previously indicated that she will update her party on her thoughts about a second vote once the terms of a Brexit deal are clear.

The director of the Common Weal thinktank, Robin McAlpine, described “an accumulation of disillusion” among activists. “There are so many faultlines, it is hard to know what direction it will go in,” he said. “The SNP members will turn up and cheer in Glasgow, but the mood could turn on something as simple as whether Sturgeon turns up to the AUOB march the day before.”

The subject of grassroots frustration was also raised by former first minister Alex Salmond on his RT chatshow on Thursday. Salmond, who has taken a less cautious approach to a second referendum than his successor, asked former Holyrood presiding officer Tricia Marwick about the Edinburgh march, which she said was evidence of “a desire for the process to be moved forward by many people”.

Marwick said: “They see [the march] as a way to put pressure on everybody involved, to say there is a case for this, we want it to move quicker.”