If after an informal discussion, your employer still refuses to furlough you, you could consider raising a grievance. ... However, the government guidance states that if your employer receives public funding for staff costs, and that funding is continuing, employers should continue to pay their staff and not furlough them.
Can I be asked to work during furlough?
If your employer furloughed you, they shouldn't have asked you to work during any hours you're furloughed - this includes asking you to work voluntarily. Your employer could have asked you to do certain types of training - for example, an online course to improve your skills.