If you are faced with the new homepage (ba.com/nx) you will need to click the link at the bottom of the flight search box on that homepage titled 'Save with a companion or evoucher' where you put in your origin, destination, dates of travel etc, see screenshot below for the link 'Save with a companion or eVoucher' (I don't yet have 5 posts on here so I can't post an image).
You should then be able to see the option to add a voucher on the booking summary page before proceeding to the payment page.

This new version of the site doesn't have the option to pay with an evoucher yet. Hope that helps!