The 90-year-old suffered serious head injuries, consistent with blunt force trauma, and a stab wound to the neck, police said.
She remains in hospital in a critical but stable condition.
Detectives from Hillingdon CID confirmed a 52-year-old woman has been arrested on suspicion of attempted murder.
She remains in custody at a west London police station.
Officers continue to appeal for witnesses and information as an elderly woman continues "fighting for her life" in hospital.
At this early stage of the investigation, officers are keeping an open mind regarding any motive for an attack.
It is not yet known if any property was taken from the address.
Detective Inspector Claire Hine said: "This was a horrific attack on an elderly, defenceless woman in her own home, which has left the victim fighting for her life.
"We are appealing for anyone who was in the area at the time and may have seen anything that could assist our investigation to come forward."
Enquiries continue to establish the full circumstances.
Witnesses or anyone with any information are urged to call detectives at Hillingdon CID via 020 8246 1552 or by tweeting @MetCC.
To give information anonymously visit Crimestoppers online or call on 0800 555 111.
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