The rose on launched on Friday after Harkness Roses rushed to make it available in time for RHS Chelsea Flower Show.
Already, 15,000 of the 25,000 available have sold and £2.50 a rose going to the charity. The rose was only named last week so it could be launched at the last minutes ahead of the show. The rose in the fastest selling in Harkness' 140+year history.
Harkness' Dave Andrews' said: "It's unbelievable at Chelsea. There's queues of people taking pictures of the QR code and ordering it. There's so much love for that lady."
Cancer campaigner Dame Deborah visited the show on Tuesday evening in a special after hours trip with her husband and TV's Sophie Raworth.
Celebrities such as Joanna Lumley, Alex Jones, Jodie Kidd, Gaby Roslin and Katie Piper had their pictures taken with the rose on Monday at Chelsea press day.
The Harkness display in Chelsea's pavilion saw the launch of 'Lady Carnarvon', a rose named after Highclere Castle's owner. Highclere is where Downton Abbey is filmed.
Three royal roses are also on display - Platinum Jubilee, Queen Elizabeth II and Duke of Edinburgh. The Queen was given a posy containing her rose and the Duke's on Monday.
The John Ystumllyn rose, planted at Buckingham Palace on Monday and the first rose named after an ethnic minority Briton, is also on display.
The Dame Deborah roses will be sent out in the autumn and more will be available in 2023.
Dame Deborah said that the honour "meant absolutely everything to me".
She said: "Flowers are a reminder of our future. We plant the seed not knowing what we might see grow.
"Being around nature gives us a lift and it is a reminder that life continues to blossom, even in some of the hardest places, and brings a smile to all of our faces, even in the hardest of times - particularly mine."
Hannah Albone, of Harkness, said of Dame Deborah's visit: “She was here on Tuesday night with her husband Sebastien. She came to our stand and had a look at the rose.
“The RHS was amazing in arranging her visit. They got some champagne and we had a little toast.
"Then Sophie Raworth took us on a tour of all the show gardens, which was amazing.
"Dame Deborah did not stay too long but it was brilliant.
“Interest in the rose has been unbelievable. Every question at the stand has been about her rose.
“It is the fastest selling rose in our 140-year history. We are expecting it to sell out very soon.
"We feel very privileged to have been given this opportunity to name a rose after Dame Deborah.
"This rose has grabbed the heart of the nation and we would like to thank everyone who has been supporting this inspirational lady to help continue her legacy in raising awareness of bowel cancer.”