Novartis said it was "extremely disappointed" by Thursday's draft decision from the National Institute for Health and Clinical Excellence.
Afinitor, or everolimus, is the first in a class known as mTOR inhibitors to be approved for post-menopausal women with advanced hormone-receptor positive, HER2-negative breast cancer.
"While the independent appraisal committee acknowledged that everolimus may offer a step change in treatment by restoring sensitivity of the tumour to hormone therapy, the evidence highlighted uncertainty relating to how much the treatment extends overall survival," said NICE CEO Andrew Dillon.
"Using the most appropriate estimates, the committee concluded that everolimus is not a cost-effective treatment option for the NHS (National Health Service)."
The Novartis drug is also used to treat patients with other types of cancer, including kidney and a rare type of pancreatic cancer.
There was better news from NICE for GlaxoSmithKline, whose drug Revolade, or eltrombopag, was recommended for use on the state-run NHS for treating the blood disorder chronic immune thrombocytopenic purpura in certain patients.
NICE also backed InterMune's drug Esbriet for a chronic lung condition called idiopathic pulmonary fibrosis.
(Reporting by Ben Hirschler, editing by William Hardy)