Hounslow Council is expected to announce funeral arrangements for the 78-year-old early next week and, such has been the outpouring of grief, a huge turnout is likely at whichever church is chosen.
There have also been calls for her remarkable life story, which has captured the public imagination, to be remembered in other ways, including a charity appeal, a bench or a tree.
The latest suggestion, made on the 'Annie Naysmith' Facebook page set up by Emma Daniels, is for a summer concert in Chiswick to celebrate her love of music.
Ms Naysmith was a talented pianist, studying at the Royal Academy of Music and performing as a young woman at prestigious venues including London's Wigmore Hall.
But her musical career faltered and she is not believed to have played a note since being evicted from her home, in Prebend Gardens, in the '60s and taking first to her beloved car and then, when that was removed, to the streets - apparently in protest at the perceived injustice.
However, those who knew her say she retained her passion for music and have recalled her singing with the "voice of an angel" both on the streets and in local churches.
She was a regular at St Michael and All Angels Church, in Bedford Park, where it is understood she often struck up conversations with the church organist.
Deanna Sewell suggested on Facebook that an outdoor concert, featuring local musicians, would be the ideal way to honour Ms Naysmith.
"Be great if we could organise a fundraiser she'd [have] liked like an outdoor concert in Chiswick (the park), wonder if it's doable. I say outdoor because she lived outdoors and a concert because she loved music xx," she wrote. "I'm sure many musicians would like to donate some time if they knew her story and I know lots of people would come."
Tributes continue to pour in for Ms Naysmith, whose way of life has elicited a mixture of fascination and respect for her fierce independence and refusal to bow to life's indignities.
Many of the recollections being shared revolve around her refusal to accept any charity, from a cup of tea to a full Christmas dinner, which was apparently left to rot on the bonnet of her car many years ago.
There have also been kind words from one of the bus drivers, who used to ferry her around despite her not having a bus pass, and others who took the time to speak to her.
Ben Halloren wrote on Facebook: "I encountered Ms Naismith many times over the last five years or so, often in the Welstead Way car park (where she set up her shelter, behind Stamford Brook tube station).
"There was usually a cheery good morning or a polite enquiry as to the time and occasionally Anne would engage in conversation, a tale of a short stay in hospital where they hid her clothes and wouldn't let her out, of local bus drivers allowing her to travel even though she had no bus pass.
"Anne had two distinct personalities and it was not unusual to hear a very vocal and heated argument taking place between the two. An indomitable and spirited lady."
He also posted a photo of a mysterious chalk drawing he said had appeared briefly in 2012 in the car park where Ms Naysmith used to shelter.
He pondered whether she had been the artist or, if not, whether her story had inspired the sketch, which shows a girl releasing a blue bird, accompanied by the message 'let it go'.
Chrissie Bladen wrote: "I used to see Annie most mornings when I worked in Hammersmith. Such a lovely lady, apparently she had been a really good concert pianist. I hope she rests in peace and is playing her piano to the Angels x."