Two polls – a first on the principle of independence and a second on the terms of any separation deal – would allow voters to fully grasp what it was they were being asked to support, Dr Alan Renwick of University College London said.

The academic said that staging two votes on the matter would not necessarily make it harder for the Yes campaign to win, as the momentum generated by winning the first poll could be carried into the second.

But the process would allow voters to have their say on the final deal reached by the Scottish and UK Governments – meaning they did not have to be “locked in” to the result of the first vote.

Thousands of independence supporters marched during The All Under One Banner event on Saturday in Glasgow. Picture: Getty

Critics of Prime Minister Theresa May’s proposed Brexit deal have long argued that it bears little reality to what most Leave supporters had voted for.

Dr Renwick said a double referendum would have allowed UK voters the chance to weigh up Mrs May’s deal with the status quo.

“A decision is democratic only if people have the information they want when deciding how to vote,” hesaid.

“Some voters will be for or against independence come what may. But for others the choice will depend on what each option actually looks like – they therefore have a right to information on this.

“Voters should not be bound, after negotiations have produced a clear plan, to the choice that they made before the options were clear.

“This is the logic that Nicola Sturgeon rightly uses when she says that Brexit would constitute a material change from what voters were told in 2014 would happen in the event of a No vote. The same logic applies the other way.”

The First Minister said last month that Scots should be given the opportunity to vote again on independence before the next Holyrood elections in 2021.

The SNP leader told MSPs that she would introduce legislation soon to set the rules for another vote but suggested she would need the agreement of the UK Government before actually holding a referendum.

However, at the Scottish Conservative spring conference over the weekend, Scottish Secretary David Mundell said that an agreement would not be forthcoming.

But Dr Renwick said any preparations for Indyref2 were a chance to “bake in” the idea of a double referendum.

“It’s fine to hold a single vote if it is clear what you are voting for,” he added.

“What’s different about Scottish independence and Brexit is that these are issues where you can’t work out the  details until after a referendum.”

Indyref2 and 3? Expert says two Scottish independence polls needed