An alternative is to purchase the cheapest ticket you can find and then just tell them that you're not flying. If this is also on a flight that has plenty of availability, you will not cost BA a dime and you will not deny anybody a seat.

I don't know what the cheapest ticket is, maybe £30?


Edit: You will of course lose £30 but after your wife is boarded, you head for GF, free dinner and lots of Bolly