London (CNN) -- A British man accused of orchestrating his wife's murder by hit men while they were on honeymoon in South Africa should be extradited to face trial, a London court ruled Wednesday.
Shrien Dewani's appeal was dismissed by Judge Howard Riddle, paving the way for extradition, said an official at Westminster Magistrates' Court.
Dewani is accused of hiring a crew of hit men to kill his wife, Anni Dewani, 28, during a taxi ride in Cape Town in 2010.
Taxi driver Zola Tongo confessed within weeks of Anni Dewani's death that he had hired two men to kill her.
In a plea deal with South African authorities, he said he was paid by Shrien Dewani to carry out the hit and to make it look like the two were the victims of a car hijacking as they were driving through a township on the edge of Cape Town. Tongo was subsequently sentenced to 18 years in prison for his part in the killing.
Speaking outside the court Wednesday, Anni Dewani's sister, who did not give her name, said the family was satisfied by the ruling, but it was just one step in the battle to find answers.
"We don't want to forget Anni in this -- for us it's all about Anni, it's all about finding out what happened to her," she said. "We will fight this battle to the end, and this battle has just begun for us."
The ongoing case has been hard on her family, she said. "Look at my mum, look at my dad -- they are struggling every day with this. They have lost a daughter."
Ashok Hindocha, the victim's uncle, told CNN the extradition decision is a relief.
"We want to know what happened. Our view on this is quite simple. There were five people in the car, four men, one lady. She was murdered," he said.
"Three of the people in the car have confessed that that they were involved and they are also in jail now for their part in this incident. Shrien is the only one who hasn't spoken. We want to know why. Why did a beautiful girl on her honeymoon have to die, to be killed, brutally murdered?"
Dewani's legal team may still seek to appeal Wednesday's ruling.
The businessman, from Bristol in southwest England, has said his wife was the victim of a carjacking and denies any involvement in the killing.
His extradition was halted last year on mental health grounds.
Psychiatric experts told a UK court last year that Dewani was suffering from post-traumatic stress disorder and depression and that he'd tried to take his life.
South African Justice Minister Jeff Radebe welcomed Wednesday's extradition ruling, saying it reaffirms the view that South Africa's legal system is fair and upholds the rule of law.
"We are also pleased that at last Mr. Dewani will stand trial for the alleged murder that induced a sense of shock and outrage -- national as well as around the world," he said in a statement.
"We guarantee him and the entire world that he will indeed receive a fair trial."
Radebe said the ruling is also a vote of confidence in the ability of Valkenberg Hospital, a psychiatric hospital in Cape Town, and the correctional services to ensure Dewani is cared for in South Africa.
But he said the ruling would not mean that Dewani would immediately be returned to South Africa, since he has further legal avenues to explore. If successful, they could lead to a further appeal in the UK courts.
Dewani's attorneys argued last year at the High Court in London that extradition to South Africa would breach his human rights under European law.
Their appeal cited concerns over the effect of extradition on his mental illness, the provision of facilities for its treatment and the risk of attack and sexual violence from other inmates.
CNN's Kim Norgaard and Victoria Eastwood contributed to this report.