Labor will have the numbers to govern in its own right in South Australia because of a surprise by-election win.

The distribution of preferences in a closely fought poll in the southern Adelaide electorate of Fisher has seen Labor candidate Nat Cook triumph.

The Liberals had been widely expected to snare Fisher but scrutineers said Ms Cook would take the seat by 23 votes over Liberal candidate Heidi Harris.

Ms Cook said she was very happy to be heading into Parliament.

"I think we'd been written off only a couple of weeks out," she said of the campaign.

"[But out in the electorate] we knew our numbers were stacking up better than everyone was saying they were, so I'm just really happy that my gut feeling was right."

Long-serving Bob Such had been the independent MP in Fisher until he died from a brain tumour in October.

He had won four elections as an independent, having quit the Liberal Party in 2000.

The ALP last held the southern Adelaide seat close to three decades ago.

Labor's state secretary Reggie Martin welcomed the result, conceding it was at least a little unexpected.

"It's been an absolute nail-biting finish. It's a great result for the Labor Party today," he said.

"We always expected a close finish but it's probably one of the closest we've had for a long time, so a little bit unexpected."

Mr Martin said the week of counting had been very closely scrutinised so he doubted any recount would be necessary, or that one would change the outcome.

Labor will have a majority in House of Assembly

With a win in Fisher, Premier Jay Weatherill's Labor team has the 24 House of Assembly seats needed to govern in its own right, after it formed a minority government back in March.

Who is Nat Cook? A local resident of the Fisher electorate, she worked at Flinders Medical Centre as a nursing co-ordinator.

A local resident of the Fisher electorate, she worked at Flinders Medical Centre as a nursing co-ordinator. She is a foster carer and did her nurse training at the Queen Elizabeth Hospital.

She is a foster carer and did her nurse training at the Queen Elizabeth Hospital. Ms Cook also worked as a retrieval nurse, intensive care nurse and in brain injury services at the Julia Farr Centre in Adelaide.

Ms Cook also worked as a retrieval nurse, intensive care nurse and in brain injury services at the Julia Farr Centre in Adelaide. She set up the Sammy D Foundation with Neil Davis after their son, Adelaide teenager Sam Davis, was killed in a one-punch assault at a party in 2008.

She set up the Sammy D Foundation with Neil Davis after their son, Adelaide teenager Sam Davis, was killed in a one-punch assault at a party in 2008. It runs a range of programs to encourage young people to reach their potential and make safe and positive choices in life.

Since the March poll Mr Weatherill snared the backing of independent Geoff Brock, then a former state Liberal leader Martin Hamilton-Smith switched allegiance.

Both men now hold ministries in the Labor team.

Labor will have 24 seats, along with the votes of Mr Brock and Mr Hamilton-Smith, while the Liberals will have 21 seats.

Mr Weatherill struck a multi-million-dollar deal to get Mr Brock's vote.

That deal was to cost $39 million in the first year in return for Mr Brock's guaranteed support on the floor of Parliament for a Labor minority Government.

Mr Weatherill said it was made up of new and existing funding and included a one-off $10 million jobs fund.

Nat Cook will be South Australia's newest Labor MP. ( ABC News )

He promised a $13.4 million annual increase in the state's regional development fund.

Ms Cook said she was confident of a continuing strong role for the independent supporters of the fourth-term Labor Government in SA.

"The majority Government is a bonus, but the independents that are in the Government are doing a great job and I have every reason to believe that will continue," she said.

SA Liberal leader Steven Marshall agreed with a view expressed by many commentators in the past week that Liberal Senator David Johnston's recent comments about defence builder ASC adversely affected the Fisher campaign for the Liberals.

Southern suburbs federal Labor MP Amanda Rishworth said the Liberals needed to get the message South Australians voters were delivering.

"Instead of washing his hands of another electoral defeat, Tony Abbott must accept his decision to send South Australia's 12-submarine project overseas, [proposed] $100,000 university degrees and a GP co-payment have each impacted on today's result," she said on Saturday.

"Instead of using weasel words to back the Abbott Government, Steven Marshall should heed today's result and repudiate Tony Abbott's assault on South Australia. Anything less is unacceptable."

A big increase in SA's Emergency Services Levy in this year's state budget has been a contentious issue for SA's Labor Government.

Ms Cook conceded it had been prominent in the minds of many voters in Fisher when she spoke with them during the by-election campaign.

She said she would take on board their views and was looking forward to putting them to her Government colleagues once she took her place in State Parliament.