The aim of this study is to establish the safety and efficacy of a combination of dexamethasone and lenalidomide (Revlimid®) (D+L) in subjects with relapsed or refractory CLL who have failed or are unable to tolerate standard up-front therapy with regimens containing Fludarabine or, in those with mutations in the p53 gene, CAMPATH-1H. The primary endpoints are: 1. Proportion of patients who achieve objective response (CR + PR) according to the updated 1996 NCIWG criteria measured at 4 weeks after the completion of chemotherapy 2. Proportion of patients suffering Grade III/IV toxicity as assessed by the NCI Common Terminology Criteria for Adverse Events (version 4.02) including an assessment of the frequency of tumour flare reactions