Six months before her death, she told a local newspaper that she had received 267 mailshots from dozens of charities in one month alone asking for her help. She already spent most of her state pension on charity donations, but felt unable to refuse every new request.
"I open and read every single one of them but my problem is I've always been one that reads about the cause then I can't say no," she said. "I have started to just put all the letters into a big box, and then I have to spend my Sunday afternoons sorting them all out ready for the recycling - but some weeks it takes even longer."
Though her body was discovered last week, her death has only just been made public by her grieving children, grandchildren and great-grandchildren.
In Bristol, friends and admirers are determined that her unstinting service to the community should be uppermost when she is remembered. One suggestion is for a public celebration of her life and the quiet, dignified impact made on so many by the woman Alastair Watson, the Lord Mayor, has this week lauded as a "city treasure".
She was best known by many for her presence, for as long as anyone can remember, selling poppies in the north-west porch of Bristol's medieval cathedral throughout the first two weeks of November. "She was always smartly turned out," said the head verger, Glynn Usher, "and would bring her own blanket and Thermos. She stayed at her post from 10 o'clock each morning to 4pm each afternoon. It can be bitingly cold, but she never budged all day and refused any fuss."
Initially, he recalled, Mrs Cooke had been one of a team of poppy sellers stationed at the cathedral, the starting point each year for the annual Remembrance Day parade, in which she always participated, to the city's cenotaph. But over the years, her vigil became a lonely one, as her comrades fell away.
Mr Usher remembered in particular the impact Mrs Cooke - who always wore the bravery medals awarded posthumously to her husband - made on younger visitors to the cathedral.
"Those two weeks in November, when she was with us, are busy weeks for us," he said. "We often have a degree ceremony for the local university and charter days for local schools. Olive loved to talk. She was always very polite, very old-school, but there were no barriers around her. I would often see her sharing her memories with the young people. There would be a great gaggle of them around her.
"What drew them to her in particular was that hers was a cheerful remembrance, if that doesn't sound odd. Obviously there was a lot of upset for her still about the tragic death of her first husband in the war, but hers wasn't a remembrance of regret, or a doleful looking back. I never heard her just telling people that they must remember. Instead she spoke of herself as a living example of someone who had lived a good life because of the sacrifice that had been made, and of her gratitude for the gift that sacrifice had given all of us in the freedom to live our lives to the full. She was a force of nature."
In fact, Mrs Cooke's connection with poppies and the British Legion predated even the death in 1943 of her husband. When she was just 16, her father, Fred Canning - who had survived active service in the Royal Irish Regiment at Gallipoli during the First World War - was one of the founders of a new branch of the Legion in the Bedminster Down area of Bristol, helping unemployed ex-soldiers find work in the local tobacco factory.
That was when she first started selling poppies, she was to recall later. "I used to stand in Bedminster with the silk poppies and the cheaper ones, as many people couldn't afford them."
After the Second World War, though she remarried and raised a family, the Bedminister Down branch became, in her own words, "my main interest". She carried the standard of the branch's women's section at the annual Remembrance Day service for 54 years until she gave it up in 1998, and then only because her arms could no longer bear the weight. And she served as secretary and later chairman of the branch, now closed.
The Legion's regional manager, David Lowe, likened her understated determination to carry on remembering, and encouraging others to do so, to that of another veteran he knew well, Harry Patch, the last surviving soldier from the trenches of the First World War, who died in 2009.
"They were, in some ways, two of a kind," he said. "Neither one of them ever wanted to draw attention to themselves or what they had done, or were doing. They were both so modest, but that was exactly what made them powerful ambassadors for their generation who could touch lives today."
Last year, having survived a brush with breast cancer, she spoke of her work. "I will never give up," she said.
It is that spirit of service that many in Bristol would now like to see celebrated. It is the sort of community activism that Olive Cooke would have applauded. "It is important," she told her local newspaper recently when it made her an award, "to think about others. We shouldn't just be looking inwards all the time, thinking of ourselves."
Although, of course, she would have insisted, that there wasn't to be any fussing over her. "In all the years I knew her," recalled Head Verger, Glynn Usher, with a smile, "the most she would ever let me do for her at the cathedral was to find her a comfortable chair to sit on".
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