Unfortunately, the food options at PHX are pretty dire, especially T4 where the BA flight boards.
Paradise Bakery is probably the lesser or all other evils.

With three hours to kill you could leave the airport. If you do, I would recommend going to Mill
Avenue in downtown Tempe (keeping north of University Drive). There are more than enough
good places to eat at (I recommend Tavern on Mill; 404 South Mill Avenue or PF Chang's; 740
South Mill Avenue), but more importantly it is less than five miles away from the airport. However,
you would have to take a taxi as the tram system is not well connected to the airport (yet).

That written, the food in F from PHX is quite good. I have never had a bad meal in F from PHX.
Also, whilst the F lounge in PHX is small they have made a lot of improvements over the past year.
At least now there are decent finger sandwiches but alas no full meals.

H