Atrial fibrillation (AF) increases the severity of, and death from, heart failure (HF). Several small studies have demonstrated that restoration of sinus rhythm by catheter ablation in patients with HF improves left ventricular (LV) function and exercise tolerance. What is unknown is whether or not AF ablation reduces all-cause death and urgent CV hospitalisations in populations with HF. The current trial will answer this outstanding question, which is faced by HF clinicians and electrophysiologists on a daily basis. AF ablation can be performed very effectively and efficiently using a cryo-balloon or radio-frequency ablation PVI technique. These techniques have evolved slowly and are unlikely to change substantially over the course of this trial. One small trial (n=363) in implantable cardioverter-defibrillator and CRT defibrillator recipients (CASTLE-AF) reported a death benefit of AF ablation but the patients were highly selected and the death reduction was far higher than real world expected differences. Recent studies have noted that the population randomised in CASTLE-AF was not representative of the general HF population with only 7% of patients in the "real world" setting meeting the trial entry criteria. CASTLE-AF is therefore provocative but inconclusive; it has made little change to clinical practice. As no studies have investigated the death benefit in a general HF population, the proposed trial is necessary and warranted. This study is designed as a randomised, open label multicentre clinical trial in which catheter ablation and medical therapy is compared to medical therapy alone in patients with HF with reduced ejection fraction (<50%) and paroxysmal or persistent AF to determine if this reduces all-cause death and urgent CV hospitalisations as well as improving QoL. By utilising the clinical and research networks of the British Heart Failure Society and British Heart Rhythm Society (BHRS) we will recruit 1200 patients. The current trial will be almost three times the size of the only previous inconclusive trial which was reported in the New England Journal of Medicine.