Hi, Mike.
Not sure I would pick those Gripping Beast figures as the base of an army for Palestine. The vast majority of pictures of Tommies in Palestine shows them in Khaki Drill, most often in shorts and shirtsleeves order, rather than the Serge SD uniforms depicted on those Gripping Beast lads.
Having said that, I shall be using some of them in such a way too, but I'm painting them up for Gallipoli (and they are going to have to bulk up the Palestine force as their second job). You could of course paint them up as being in Khaki Drill, but as already said, most of the time if wearing KD troops seem to be in shorts. You do however see some odd combinations, such as serge trousers with a KD jacket (and vice versa), and occasionally troops in KD trousers and jackets. Some enterprising LAFer also posted some pics of troops in Palestine clad entirely in serge SD a while back, though the pictures were post-war ones.
So in conclusion, while I don't have any problems using them for Palestine, I don't think I'd want my
entire force dressed that way, as it doesn't seem typical of the way the troops dressed there. But that's just me.
These are the books I mostly turn to for this type of thing:


I also found these pics while surfing the other day, which show troops in the Dardanelles in the serge uniforms, like those the Gripping Beast fellows are wearing (and even showing the Royal Naval Division, which you can get a head for from GB now):


(Not sure about the red stripe on the trousers.)