I just did it! I called the BA team and explained the situation. They said I will get a full refund under the 24hr rule. I didn't even know it existed! Good thing I called them now, the booking was made yesterday at 4pm, so just in the nick of time. Phew!

The funny thing is for this flight, the pricing is in the following order: Economy > WT+ > CW! Economy was something like £1080, while the CW was £700. WTH??