Alistair Darling and Alex Salmond will go head to head on 25 August, as 700,000 postal votes are sent out for the referendum

The next televised clash between Alex Salmond and Alistair Darling on Scottish independence is to be screened live across the UK later this month.

The BBC said it has reached agreement to stage the second head-to-head debate between the yes and no campaign leaders on 25 August, live from the Kelvingrove art gallery in Glasgow.

The BBC said the 90-minute event, which will include a 200-strong audience of yes, no and undecided voters, would be aired on BBC1 in Scotland and simultaneously on BBC2 in other parts of the UK. Live streams will also be shared with other broadcasters, including Sky.

It will take place just as upwards of 700,000 postal votes are due to be sent out for the referendum – the largest number ever seen in Scotland, and equivalent to roughly 20% of the expected turnout in next month's referendum.

The first live debate between Salmond, Scotland's first minister, and Darling, chairman of the pro-UK umbrella group Better Together, drew an estimated audience of 1.7 million viewers on STV in Scotland and online last week.

But STV and its sister station in the rest of the UK, ITV, were criticised after ITV refused to screen the debate on television outside Scotland, leaving viewers outside Scotland to rely on STV's online player, which was at first unable to cope with demand.

Meanwhile Sky News has confirmed it is in talks with both teams about staging its own event, but without a studio audience. It would use innovative digital and social media techniques to build a live audience online, using Twitter, Facebook and Google.

The channel is still searching for a suitable date but there are doubts the event will take place. Salmond's advisers are said to be sceptical that a digital audience will give them the reach the yes camp needs, or access to the undecided voters needed to swing the result.

STV's success in landing the first debate embarrassed BBC executives, who had been in protracted but unproductive talks as both sides wrangled over the timing, location and date of the event.

Salmond rejected two earlier dates suggested by the BBC. The yes campaign had been keen to agree a date closer to the referendum on 18 September, hoping Salmond could give the yes vote a lift in the closing stages. Better Together was adamant that Darling would only debate with Salmond before postal votes go out.