There are three Officer casualties in Medjez el Bab War Cemetery

One Captain, one Lieutenant, one 2nd Lieutenant.

Three casualties died the same day, 31st March 1943, one Lieutenant, two Bombardiers these could quite possibly have been in the same vehicle as your father when they either struck a mine or were hit by a shell. A Reconnaissance vehicle or a Forward Observation Officer team normally used a Universal Carrier ( aka Bren Carrier) at this time and could have been carrying four (but most likely three) i.e. driver/ signals, FOO  and Observer Assistant.

The Lieutenant was killed on 13th April

If he was simply driving an officer from a to b (most unusual) then it would be most likely the Captain who was killed on 26th April 1943  the last and one of the heaviest days fighting at Gueriat el Atach.

A Gunner was killed (or died) on 10th May 1943

Do you have the names of the men on the service booklet. We are looking at  the above dates.

You could ask on the other site that I mentioned for pages from the 19th Field Regt War Diaries to see what happened on the dates that the officers died.

Hope this helps