Amending. You can book your Companion Voucher redemption in whatever class you find available and then upgrade it if flights open up in a higher class for ?35 per person each way. You have to call BA to do this and cannot do it online.

Traditionally, you cannot "upgrade" a British Airways American Express Companion Voucher using Avios once the booking is made; however, the rules depend on the type of voucher you hold. If you have a voucher from the free BA Amex card, it is restricted to Economy (World Traveller) only, and you cannot use it for any higher cabin. If you have the "Premium Plus" voucher, it can be used for any cabin (Economy, Premium Economy, Business, or First) at the time of booking, provided there is "Reward Flight" availability. If you have already booked an Economy flight using a Premium Plus voucher and want to move to a higher cabin later, you generally cannot just "pay the difference" in Avios; you must instead cancel the original booking (subject to a £35 fee) and rebook the entire trip in the desired higher cabin, assuming seats are available. It is also important not to confuse this with the "Barclays Cabin Upgrade Voucher," which specifically allows you to book a seat in a higher cabin for the Avios price of the one below, but functions entirely differently from the Amex Companion Voucher.