She now wears killer heels, designer suits, has a sexy British lover, and so much money from making speeches to business conferences and sitting on global company boards that home has become a massive apartment on Copenhagen's waterfront.

The third series of Borgen – the political drama that has been fascinating audiences in 70 countries, including the UK, and is credited by a Copenhagen Business School study with stimulating debate and combating Danish voter apathy – starts on Saturday.

It features a very different Birgitte Nyborg (Sidse Babett Knudsen). Think Tony Blair. She is enjoying all the trappings due a successful, celebrated ex- prime minister after losing a general election two and a half years previously at the end of Borgen 2.

But it does not take her long to decide that the Danish Moderate party which she led is deviating too far to the right, with harsh immigration policies under her old rival and crown prince, Jacob Kruse. So she decides she is still a politician and makes a leadership challenge.

Her decision paves the way for one of the most compelling strands in this, the final series from DR (Danish Broadcasting). She asks the successful newscaster Katrine Fønsmark (Birgitte Hjort Sørensen) to become her press secretary, creating a fictional partnership of two strong women, at different stages in their lives, attempting to start a new party.

As Sørensen noted at a Bafta screening in London attended by the stars last week, in the past series they had only a few scenes together, mostly professional ones based around TV studio interviews. This time it is different.

But Katrine has changed, too. She has had a baby fathered by Kaspar Juul (Pilou Asbæk), the former spin doctor, though they lead separate lives, sharing childcare of Gustav. Katrine is shown parenting in a flat now cluttered with the baby's things. You see her stressed, snapping at her mother for moving nappies, with the baby asking for Grandma first when he's upset because she looks after him so much.

Katrine's mother opposes her decision to quit broadcasting for politics, reminding her she is a single mother. But Katrine goes ahead anyway.

Sørensen said that Borgen's appeal lay in making the politics accessible and its mix with personal lives: "It's a combination. Two strong female leads seem to resonate here [in the UK]. In Denmark we are slightly further ahead in gender equality. The choice about having children, it is harder in the political system in Britain. There is a scene in the second episode when Katrine brings her child to work and it is accepted."

Divorce is also depicted as working smoothly, not a source of conflict. Nyborg's ex-husband, Phillip Christensen, has moved from Copenhagen's Business School to become vice-president of a Danish investment bank. He and Nyborg have a calm relationship, and their children, Laura and Magnus, are doing well at school. Nyborg's lover, Jeremy, an architect (played by Alastair Mackenzie from Monarch of the Glen) is also divorced, discreet and adoring. Episode one begins with them meeting in Hong Kong. "I came in late and got to kiss the prime minister," he quipped at the screening (although the writers' decision to give Birgitte a lover, a new Phillip, led some Danish viewers to criticise a deviation into soap opera).

Knudsen said the rules about the mix of politics and personal life in Borgen were not calculated as an exact percentage: "The way we deal with it, I read the scripts, the writers know everything about politics. I say, I don't understand. We find a balance, where I always understand. The intellectual papers think it's like a cartoon, but it's very difficult, mainstream politics is so complex. The scripts are fantastic, but I changed a lot."

One key area to simplify was the process of setting up a new political party – not that uncommon in Denmark – for which the writers had written a fictional guide. She added that, despite all the anxieties Borgen had stirred in the media and political classes in Denmark, "the big issue" in series three when it was screened in January and February was an episode about pig farming practices: cutting off a pig's tail.

Nadia Kløvedal Reich, the DR executive who is head of fiction, confirmed that the business school study showed more engagement, but not changes in party allegiances. She said another controversial episode was about prostitution, which led to a Danish MP in the conservative People's party being criticised for advocating a bill of rights for prostitutes – inspired by Borgen.

Lars Knutzen, who plays Birgitte Nyborg's adviser, said that the clue to Knudsen's acting is that "she is a great comedian in Denmark, she's not a mainstream actor, that's the challenge to work with her. She's really not a traditional actor." After one scene had been shot, he said, she had "taken out false teeth from her pocket and put them on. Clowning around, she brings the humane quality to the politician which we needed."

The series also opens up a seam of media politics. The fictional TV1 broadcaster has a new programme director in his mid-30s, who sees TV as a product, quite different to the predominantly news-driven media. He views news director Torben Friis's public service vision of journalism as anachronistic, urging him to look at the cost benefits of substituting political debate with imported entertainment. Katrine is then advised by veteran journalist Hanne not to stay late because of office politics and go home to her child.

With DR only able to afford to make about two series a year of original drama, Reich said there was no question of Borgen coming back or of DR deviating from its public service mission to concentrate all its creative energy on original writer-led drama that reflects Denmark. A third series of the Danish/Swedish crime co-production The Bridge has yet to be agreed.

Reich added that DR is diversifying its mix. In January it launches a 10-part series, The Legacy, a character-driven drama about a modern family and the impact of the permissive 1960s, with a second series ordered.

It will also run 1864, a historical drama about Denmark's most bloody war with Germany. But it is adding in a new strand, a 16-part, 30-minute comedy drama about a modern Danish man. It has also agreed to make a 20-part drama, Follow the Money, about financial fraud. "It is another flavour from The Killing, not so many murders," Reich said.

The final series of Borgen begins on BBC4 at 9pm on Saturday 16 November