A British court has granted the woman anonymity, but she reportedly comes from a wealthy family in Saudi Arabia, and is married to a member of the royal family. (Her husband and her relatives have cut off contact with her.) Her fears of stoning are not unfounded — 40 women have been executed in Saudi Arabia since 1990, and one currently awaits stoning for adultery. (She had a child six years after her husband died.) Another princess, Mishaal bint Fahd, was executed by "gunshot to the head" after admitting adultery in 1977. After a British documentary was made about her execution, the Saudi government expelled the British ambassador, pulled members of their royal family out of Britain, and canceled lucrative export contracts.
It is likely fear of such retaliation that makes the British government keep asylum deals like the princess's a secret. Robert Verkaik of the Independent writes that to make public such deals "would in effect be to highlight the persecution of women in Saudi Arabia, which would be viewed as open criticism of the House of Saud and lead to embarrassing publicity for both governments." (Interestingly, the Obama Administration, as reported last week, is softening the United States' stance on granting asylum for victims of domestic abuse.) But in keeping secret Saudi Arabia's human rights abuses, Britain is essentially protecting the Saudi government from any international pressure to change.
Note: The Muslim pilgrims pictured are stoning a pillar as part of a religious ceremony; they are not participating in an execution.
Princess Facing Saudi Death Penalty Given Secret UK Asylum [Independent]
Saudi Princess Given Asylum In UK Over Fears She Faces Execution For Having Illegitimate Child With British Lover [Daily Mail]
Saudi Arabian Princess Seeks Asylum In Britain Over Illegitimate Child [Telegraph]