The contract came into existence at the moment that the employer offered you work and you agreed to work there. (There's no need for a contract to be written down. Every time you buy something online or in a shop, for example, you enter into a contract with the vendor. Similarly, every time you park your car in a car park you enter into a contract with the owner of that car park).
A 'written statement of employment particulars' isn't the same as a contract but it includes elements of it.
Yes, you can be furloughed but it's not automatic. It's up to an employer as to whether he/she chooses to use the scheme or not.