I noticed a lack of Wild Beasts tabs on this site. Here is more or less how Tom plays
the guitar on All The King's Men. There are just a few chords and they are finger picked,
I'm not sure about the finger picking pattern, but play around with it and you should be 
able to figure out something that sounds nice, even if it's not exactly the same pattern
as the original.

I figured this out from studying a few live performances, and I'm pretty sure the tuning
is correct and everything is fairly accurate. The other guitarist (Ben) plays his part
as well, but I haven't figured that out. You can just play Tom's part all the way 
through if you're playing by yourself.

Tuning: D G C G Bb D
So basically from standard tuning, detune the 6th, 5th, 4th and 1st strings by a whole
step, leave the 3rd string as it is, and detune the 2nd string half a step.

Intro:
D |0------0-----0------0------------|
Bb|9------0-----0------0------------|
G |0------0-----0------0------------|
C |10-----10----12-----10-----------|
G |8------10----12-----10-----------|
D |10-----8-----10-----8------------|

Verses:
D |7-----7--------------------|
Bb|9-----9--------------------|
G |10----7--------------------|
C |7-----7--------------------|
G |7-----7--------------------|
D |8-----8--------------------|

So you're basically just lifting your smallest finger up and down off the 3rd string
during the verse.

For the chorus (when he starts singing "Now no one will find your limit..."), play the
same chords from the intro once. Then, play the 3rd and 4th chords from the intro over a
few times. After the last chorus, end on the 3rd chord from the intro.

That's pretty much it, let me know if you have any corrections!