According to today’s Guardian, the advice is clear, you can undertake training while on furlough during the current Corona Virus lockdown.
Training is allowed, but only if it does not provide services to, or generate revenue for, the employer. It must also be directly relevant to an employee’s role and must be first agreed between the employer and the employee.
Follow the discussion attheguardian.com/money/2020/may/03/furloughed-from-work-it-pays-to-know-your-rights