More than 1 million voters have signed a declaration in favour of Scottish independence, according to the pro-independence campaign Yes Scotland.

When the yes declaration was launched along with the official yes campaign in May 2012, the first minister, Alex Salmond, said that if the target of 1m signatures was reached by the referendum then Scotland would become an independent country.

The chief executive of Yes Scotland, Blair Jenkins, described the announcement as a milestone, insisting that many more people would be voting yes than had signed the declaration.

"This was always intended as an indicator, a way of demonstrating the strength of the campaign and also to give our volunteers something to aim for," he said at an event in Edinburgh, also attended by the Proclaimers, a Scottish band supporting independence.

The Scottish electorate for September's referendum is about 4.2 million people. If turnout reaches 80%, as many – including Salmond – now confidently predict it will, this translates into 3.36m votes. The yes campaign still needs well over 1 million supporters to swing the vote on 18 September.

Jenkins also confirmed that Friday morning's total of 1,001,186 signatures had been checked against the electoral register. Concerns had been raised earlier in the campaign that people were signing in duplicate, or with invented names. "At an early stage a few people came on with funny names," he said, "but it's been checked and double checked and we are confident."

He said he would consider releasing the list to a third party for independent verification, although there were confidentiality issues involved.

Speaking at the event with his twin brother Craig, Charlie Reid, of the Proclaimers, said he hoped undecided voters would look at what the independence campaign had to offer. Returning to what has recently become a major theme of the yes campaign, he said: "People say there are uncertainties about voting yes, but there are real uncertainties about staying in the UK."

Asked about the thrust of the yes campaign in the final weeks, Jenkins said: "We have always placed more emphasis on the positive advantages of independence, but we have also known we had to be very clear about how badly served people in Scotland are by Westminster and about the very real threats to the public services they care about from austerity."

Asked if they would write a song to celebrate a yes result, the Proclaimers were circumspect but confirmed they would stop playing their pro-independence anthem Cap in Hand.

Meanwhile, speaking to an invited audience in Glasgow alongside the Scottish Labour leader Johann Lamont, Gordon Brown urged voters to "think twice" before voting yes, warning that oil revenue would only sustain a "fraction" of public services if Scotland left the UK.

With healthcare a key battleground in the referendum campaign this week, Brown said: "As a result of sharing the resources of the health service across the United Kingdom – and it is time the Scottish National party admitted this – £900m and more is spent on the health service in addition to what an allocation based on population would allow."

"Why should we throw all this away, especially when we can spend the money in Scotland in any way we choose?"