Premier Jay Weatherill says he will apologise to the family of a British man after authorities refused to recognise his same-sex marriage on his death certificate.

Key points: Briton David Bulmer-Rizzi was honeymooning in Adelaide with husband when he died

Briton David Bulmer-Rizzi was honeymooning in Adelaide with husband when he died SA does not recognise same-sex marriages from overseas

SA does not recognise same-sex marriages from overseas "Never married" was marked on death certificate

"Never married" was marked on death certificate SA Premier says legislation will be introduced into Parliament to deal with these issues

David Bulmer-Rizzi, 32, was killed in a freak accident in Adelaide, while honeymooning there with his husband Marco.

The couple were married in the United Kingdom last year, but under South Australian law their marital status was not recognised.

It means David Bulmer-Rizzi's death certificate was stamped "never married".

"When the funeral director came that's when I was told that because Australia doesn't recognise same-sex marriage, it [the death certificate] will say 'never married'," Marco Bulmer-Rizzi told Buzzfeed News.

"I asked at that point whether it was possible to say nothing [about his marital status], and I was told, 'No, that's not one of the drop down options on the computer'.

"I couldn't refuse. There was nothing I could have done. They wouldn't say married. They wouldn't leave it blank. They would only say, 'never married'. This was confirmed by email because we complained afterwards."

Mr Weatherill told the ABC he wanted to offer a personal apology to David Bulmer-Rizzi's family.

He said the family's experience underscored the hurt caused by senseless discrimination.

"It is another example of how senseless discrimination of sexual orientation can cause pain and hurt," Mr Weatherill said.

Marco and David Bulmer-Rizzi were married in the United Kingdom in 2015 before having a full ceremony in Santorini, Greece. ( Facebook )

Marco Bulmer-Rizzi said the marriage not being recognised caused further troubles.

Because he is not recognised as his husband's next of kin, all funeral arrangements and decisions had to be approved by Marco's father-in-law.

"I was completely overlooked," he said.

"I wasn't the next of kin. Every single question I was asked — whether or not I wanted David cremated, whether or not I wanted David to have a service, or be washed, even the cost of the coffin they were to use — after I gave my answer David's father was consulted.

"He was also specifically asked, 'Do you want to look this over before it's signed?' It was outright discrimination. If I didn't get on with my in-laws I don't know that I would have any rights."

Bill to remove discriminatory laws introduced to SA Parliament

Last year a Government report revealed hundreds of pieces of discriminatory legislation against gays, lesbians and women.

Mr Weatherill said a bill to change those laws would be introduced to Parliament later this year.

"We introduced an initial Bill to the Parliament last year to begin the removal of discrimination from South Australian legislation," he said.

"We will introduce a further raft of legislation to the Parliament this year that will grapple with the more complex issues such as this."

Australian Human Rights Commissioner Tim Wilson said it was disappointing South Australia was behind other states in removing discrimination against same sex couples from its legislation.

"It's also disappointing that it's taken a man's death and the shock and horror that must be going through the minds of the father and of this man's husband that their relationship will never be fully recognised in the documents and records related to end of his life," Mr Wilson said.

South Australian Senator Penny Wong called on Federal Parliament to legislate for marriage equality.

"This case is a tragic example of how Australia's marriage laws discriminate against gays and lesbians, causing needless pain, suffering and heartache," Ms Wong said.

"It shows why Federal Parliament needs to legislate for marriage equality and bring Australia into line with countries like the United Kingdom.

"Our sympathies go out to Mr Bulmer-Rizzi at this difficult time."