Women in Saudi Arabia will be notified by text message when they get divorced, according to a new law that came into effect on Sunday.

The new law is being seen as a way to end secret divorces and ensure women are fully aware of their marital status so they can protect rights such as alimony.

The move comes as Crown Prince Mohammed bin Salman (MBS) has started to give women more rights in the conservative kingdom, which included lifting a ban on women driving last year.

"Saudi courts have started to send such (divorce) notifications ... a step aimed at protecting the rights of female clients," the Saudi Ministry of Justice said in a statement on their website.

It said women could check their marital status on the ministry's website or visit the relevant court to get a copy of divorce papers.

"In most Arab countries, men can just divorce their wives," said Suad Abu-Dayyeh from global rights group, Equality Now.

"At least women will know whether they are divorced or not. It is a tiny step, but it is a step in the right direction," she told the Thomson Reuters Foundation by phone.

But Abu-Dayyeh said knowing about divorce does not mean a woman will get alimony or the custody of her children.

In recent years women in Saudi Arabia have been allowed to enter sports stadiums for the first time, vote in local elections, and take a greater role in the workforce as Saudi Arabia tries to diversify its oil-dependent economy.

But many Saudi women have taken to social media to push for more freedom, including protesting against the country's strict dress codes that require women to wear an abaya - a loose, all-covering robe - when in public.

Campaigners said the main sticking point remained Saudi Arabia's guardianship policy, whereby women must have permission from a male relative to work, travel, marry, and even get some medical treatment.

"The male guardianship system is a core issue and it must be dismantled. It controls women in each and every step of their lives. This system strangles Saudi women," said Abu-Dayyeh.

Although many have hailed the Saudi government's reforms, these have been accompanied by a crackdown on dissent with about a dozen female activists arrested.

In November, rights groups Amnesty International and Human Rights Watch accused Saudi Arabia of torturing and sexually harassing some jailed female activists - allegations denied by a Saudi official to Reuters.

A group of British parliamentarians and lawyers on Wednesday requested an "urgent response" from the Saudi ambassador by January 9 to allow them to speak with the held activists.