No. The free shares are in a Share Incentive Plan(SIP) and can only be sold 3 years after their allocation date with tax and NIC’s to pay, or after 5 years tax free. Unless you’re a good leaver!
The SAYE shares are yours do to what you want with, the day you buy them. The corporate nominee account is just a holding account for those shares and any you may have bought yourself via Equiniti at the time of privatisation. There are no conditions on when you can sell your SAYE shares.