[AaronLancs]

Just doing a quick look over on UK Gameshows. Wouldn't this become Potato's first ever commission for the BBC?

Seems like it. The only non-ITV show listed is Four Weddings, which aired on Sky Living.
www.ukgameshows.com 

However, 12 Yard is owned by ITV as well, and they have done BBC shows.

I'd say with 12 Yard the thing is that they were established under Hat Trick and then later sold to ITV Studios rather than being a direct creation under the Studios umbrella.