Marian Botos, 70, was attacked outside her home on Saturday, 7 November only a short while after she had been selling poppies for in Harrow Town Centre, before going shopping.
She suffered a serious head injury.
Detectives have pleaded for the public's help to find a suspect, who is described as a white man, aged in his late 30s and 5ft 8ins tall. He was wearing a grey or dark coloured top, black trainers and a dark coloured hat.
Police said it is believed that he fled the scene in a white car-derived van.
A police statement said: “Marian was assaulted at the location (in Stanmore) at around 7.10pm on 7 November after she had caught the bus home from shopping in Edgware.
“She suffered a serious head injury during the robbery and remains in hospital in a critical condition. Earlier that day Marian had been selling poppies in Harrow Town Centre, before going shopping. Her handbag has not yet been recovered.”
Detectives are trying to trace the bag, pictured above left, which is described as slim with a brown leather look, rectangular in shape, in a clutch style with a zip top and long thin shoulder strap.
There were various items including a black purse with metal clip fastening, black fabric gloves and red lipstick.
Detective Chief Inspector Andy Chalmers, from the Homicide and Major Crime Command said:
"Marian remains in hospital in a critical but stable condition. She was practically on her doorstep when she was attacked and robbed of her handbag and I would urge anyone who may know something that may help us catch the person responsible then please get in touch."
"We are urging anyone who recognises this handbag to come forward and help us with our enquiries. It is fairly distinctive someone may have found it discarded in the street or saw Marian's attacker in possession of it when he fled the scene.
Two men were arrested by officers from Harrow on suspicion of robbery on Friday 13 November, after a vehicle stop in a street and have since been bailed pending further enquiries.
Anyone with any information is asked to contact the Incident Room on 0208 358 0100, or call Crimestoppers, anonymously, on 0800 555 111.