The reason why prescribed information can’t be signed together with contract is because prescribed information needs to be sent to tenant after protecting the deposit, therefore the only compliant way to do it is after deposit is paid and protected. 

This is clearly laid out in the legislation: 

https://www.legislation.gov.uk/ukpga/2004/34/section/213#:~:text=The%20information%20required,by%20the%20landlord.