A large number of household items were dumped at Morton Cemetery, in Riddlesden, West Yorkshire, last week and discovered on November 19.
Among the items dumped were an old mattress, a cot and bags of rubbish. Bradford Council, which owns and runs the cemetery, has since cleaned up the mess.
Captain Sir Tom Moore, who captured the nation's hearts when he raised millions of pounds for the NHS during lockdown, was buried at the cemetery in July following his death at the age of 100. He grew up in Keighley, and was buried in his family's plot.
Vivienne Hills said she was "saddened and appalled" when she saw the mess while walking her dogs.
She said: "Whoever is responsible, why did you have to deposit three loads of rubbish to blight this beautiful place? You have solved your problem, but created one for someone else.
"You have acted in a disrespectful and inconsiderate manner. The grounds are always immaculately kept, why did you feel the need to change this? Anyone visiting a grave is entitled to do so without feeling that their privacy and tranquility have been invaded.
"You should be ashamed of yourself."
Councillor Julie Adams, who is chair of Keighley Town Council, also said she was appalled by the fly tip.
She added: "I’m given to understand that the cleansing team from Bradford Council have now cleared the waste. It’s pleasing to see that in this instance, they’ve responded so quickly."
A spokeswoman for Bradford Council said: "The rubbish has now all been removed and we will be investigating the incident in line with our environmental enforcement policy."