In this clinical research trial, we explore whether the cholesterol-lowering drug simvastatin can improve treatment given for cancer of the rectum. Rectal cancer is often treated by combined chemotherapy and radiation, before surgery is performed to remove the cancer several weeks later. However, if the cancer is not sensitive to this treatment (which happens in more than half the patients), the risk of cancer relapsing is much higher. Retrospective studies show much better cancer responses and fewer short-term and long-term side effects in patients taking a statin drug during radiation for a variety of cancers, including rectal cancer. This study with 222 NZ and Australian patients will test if taking a simvastatin tablet every day for 3 months (during combined chemotherapy and radiotherapy treatment and for 6 weeks afterwards) can improve the rate of good tumour responses on MRI scan and reduce the side effects of these treatments.