Police were alerted to the attack by the ambulance service after the woman, thought to be in her 30s, was found outside St Margaret’s Church on Walgrave Road.
She was rushed to hospital with serious injuries and remains in a critical condition after the attack at around 3.15am.
Part of the church is closed as forensic officers investigate.
Various media reports have suggested that a large knife or ceremonial sword was seen being carried away from the area by detectives.
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There have been no arrests.
Anyone with information has been asked to call police on 101, quoting log 392 of 8 April. Witnesses can also call crimestoppers anonymously on 0800 555 111.