This is a phase II trial to assess whether IRESSA™ (gefitinib) has anti-tumour efficacy in patients with breast cancer. The trial proposes to enter 27 patients who have acquired resistance to tamoxifen and 27 patients with ER negative tumours. However for each of these two types of patients recruitment will stop after 14 patients have been entered in order to confirm that IRESSA™ (gefitinib)has anti-tumour efficacy. If no patient out of 14 in a group has shown clinical benefit (ie an objective response (CR or PR) or stable disease (SD) for at least 24 weeks) then a clinical benefit rate of >20% can be ruled out with >95% certainty. If one or more of the objective response or stable disease (> 24 weeks) has been seen in the first 14 patients recruited in a group then recruitment to that group will recommence to a total of 27 patients. If 14 patients are entered into an arm but not all 14 patients are available for final analysis and the toxicity/safety and tolerability profile of the therapy is acceptable and documented and a clinical benefit is seen in the patients, enrolment of additional patients beyond the initial 14 may be made based on overall clinical assessment.