Sorry to hear your employer is being difficult. They’re obliged to follow health and safety guidance – which includes protecting you from the virus if you’ve been identified as a vulnerable person. However, they don’t have to pay you sick pay (as you’re not sick).
You can – and should – ask them to furlough you, instead. If they refuse, you may have grounds on a discrimination case if your chronic condition (which has led to the Govt advising you to shield) is considered a disability. This means it must have a long-term impact on your daily living – which , for most people advised to shield, is the case.
Let us know how you get on!