Catherine Smith was found covered in blood in Lydhurst Avenue, south London sometime on July 27, the BBC reported.
She first saw her attacker while walking her dog near Streatham Hill, police said.
The attacker - described as a slim, white woman, followed Smith and was waiting for her when she arrived home.
The woman repeatedly asked Smith for money as she entered her house, according to police.
Later the woman rang the doorbell and asked if she could use the toilet. When Smith refused, the woman forced her way in pushing her to the floor, causing her to hit her head, the report said.
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The suspect then ran off, the report said.
Smith's cries for help alerted a passer-by who came to her aid. She was taken to hospital with serious injuries and has since been discharged.
Scotland Yard said: "This was a vicious unprovoked attack on an elderly, vulnerable woman's own doorstep. The attack has left her very distressed.
"We believe the suspect spotted Catherine in Palace Road Nature Gardens and for unknown reasons decided to follow her home, harass her and then brutally assault her," it added.
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