Assuming the red/yellow bands indicate RAC, then I have 1st Recce Regt., RAC & 4/7th Royal Dragoon Guards listed as divisional troops belonging to 1st Infantry Division while in Palestine (the latter were in the middle east from 1946 until 1952, it seems).
As for 1st Div. slip-ons, I know of two other combinations:
Which was my Dad's in Palestine c. mid-1947 (I believe when 2nd Battalion, The Royal Lincolnshire Regiment was transferred to 61st Lorried Infantry Brigade (then attached to 1st Infantry Division)).
On a display in the Lincs. Regt. museum, representing the CO's runner (Stick Orderly) at Battalion HQ, Canal Zone, Egypt, c. 1950 (Stephen also has some like this).
By the way, I'm sure I've read somewhere that the red triangle backing to the 1st Div. sign signifies post-war (possibly mid 1950s onwards, I seem to recall was claimed) - does anyone know if this true or not?