No. You can cancel the ticket (by talking to a human) and you'll have the Avios and Copmanion Voucher refunded to your account, plus the taxes paid (minus the £35 per person cancellation fee - assuming this is cancellation made out of choice rather than a BA cancellation). Then you can rebook (on the same call) using that same voucher and Avios.

OR - You can cancel your current booking online to generate an FTV where the voucher, and all Avios and taxes paid would be wrapped in a voucher. You'd then need to call up to use this voucher. However - whilst it's usually instant - it can take up to 7 days for an FTV to be issued.

The second option is favoured by those who would not get their companion voucher back if they used the first refund option (because it would have expired).