The uniform doesn't seem to have changed much in the interwar years. Their Sunday best seems to have remained a tallish red fez (which was retained into the post-WWII period), but in the field it would appear they continued to wear the low pillbox cap seen in WWI, though usually without the neck flap that the figures always seem to have. To be fair, though, most photos I've seen of them in WWI show them without neck flaps, too. I've long wished that figure manufacturers would leave them off, as you have a devil of a job trying to remove one from a figure without ruining it.

In WWII they were more often in long trousers and wearing brimmed bush hats. That's their typical look for E Africa in WWII (though I have seen pictures of them in shorts and also with tin helmets). Photos of them in Madagascar have them in tin hats, and jungle green and bush hats for Burma.
Due to a lack of newsworthy engagements in the interwar years, pics of them on campaign in this period are pretty sparse, so I'm not exactly sure at what point the change in uniforms occurred. Wouldn't surprise me if it didn't happen until the war itself. A big conflict is often the thing that spurs on a change in gear.
Think I'd use the WWI Brigade ones, personally. Not sure of their UK availability currently, mind.