It is indeed The Temper Trap. I bought their CD and was fascinated with their sound.
To go on further, I do think the pedal that perhaps Alan you say is a 4 button amp switch, do you not think it could be this:
especially if you look at the first picture, you can kinda see the shape.
And then I got one final theory that the pedal right in his left front hand corner is the: Holy Grail Reverb, I think its this cause I see the big black knob (on the last picture), and it looks bulky like the Holy Reverb
But that just leaves that one last black pedal on the top of his pedal board, next to the Tubescreamer... What the heck is that?
*Oh wait, I just saw another pedal that I never noticed before - On picture 2, with him holding the pedal board, under his arm, you see an orange pedal?