The main aim of this study is to test the safety of acadesine in patients with B-CLL and see what effects it has on patients and their leukaemia. The study also aims to examine the way acadesine is processed by the body. The study will look at the effects of acadesine in the body and the concentration of the drug and its main by-product (ZMP) in the blood to determine the dose and the frequency of dosing that is likely to be the most effective.