Can a zero hours supply teacher employed by a school be furloughed?

starbugged

I'm a supply teacher who has a zero hours contract directly through the school, which is part of a small academy trust. I haven't worked for them for a few months, but my contract is still active on their payroll. As the school has almost no students at the moment, they obviously don't need a supply teacher, so I asked if I could be furloughed. They replied with: "I have checked with our CFO of the Trust and she informs me that we are unable to pay you as you were not contracted to work for the school, we are unable to apply furlough for our staff as we are publicly funded."

Are they saying that they can't furlough me because the school is effectively still open, and they are still paying their staff? Is it definite that they are unable to furlough me?

Thanks for your help. Stay safe!