This study is for patients with malignant mesothelioma of the lung lining (called pleura) who have had previous chemotherapy with a platinum-based regimen whose disease has progressed. Malignant pleural mesothelioma (MPM) is an aggressive, frequently drug resistant, and incurable disease that is increasing in incidence in the UK and worldwide. All patients with MPM will relapse following first line chemotherapy and at present, there is no standard treatment available for patients in the second line setting. The vinca alkaloid chemotherapy drug vinorelbine has shown promising activity in a single arm UK trial. However to date, there has been no randomised evaluation of vinorelbine in mesothelioma in the second line setting. In addition, there have been no trials which have looked at underlying molecular changes in mesothelioma which may predict vinorelbine efficacy; This might allow vinorelbine to be used in patients only where there is a chance of benefit. Studies suggest that vinorelbine requires a gene called BRCA1 (shown to be absent in 38% of mesothelioma cases) in order to induce cell death in mesothelioma. The VIM trial aims to establish whether vinorelbine in patients with MPM helps them live longer and whether the BRCA1 gene is helpful in selecting patients most likely to benefit from treatment.