The main aim of this study is to test the effectiveness of radiotherapy for marginal zone lymphoma that has developed outside the stomach. The treatment that is given in the trial is standard therapy but information on the response to treatment and the side-effects associated with treatment has never been collected before in a large study in which patients all received the same treatment and were closely followed up afterwards. The second aim of the study is to look at factors that might cause marginal zone lymphoma. Often this type of lymphoma can be associated with infection in the stomach with a bacterium called Helicobacter pylori. Each participant will be tested for the infection using a breath test. Treatment for the infection will be offered if H. pylori infection is found. There have been reports of disappearance of this type of lymphoma just with antibiotic therapy when there has been H. pylori infection in the stomach, even if the lymphoma was growing another part of the body.