I have been placed on furlough but unpaid furlough due to being placed on payroll too late

hb2

Companies can fire during furlough. Your normal contractual terms apply but, as has been said, you have very few statutory rights as you started very recently. If you believe that there is no future for you with this company, it is probably a good time to start looking elsewhere, while there are still companies (like supermarkets and delivery firms) wanting extra staff.

silvercar

To put you on furlough the company needs your agreement as it is a change in your contract. Without that agreement, the company needs to pay you your contract rate. As a new employer it could give you minimal notice, but would need to pay you in full since the start of your contract.
Furlough rules mean they must agree to pay you at least as much as they are claiming back from the government, but if they haven't changed your contract they need to pay you - whether or not they claim it back.