There is much nonsense written and spoken about the Battles of El Alamein. The planning for the three battles (inc. Alam Halfa) was undertaken by Auchinleck and his Chief of Staff, Eric Dorman-Smith (later changed to O'Gowan). Montgomery took the plans and presented them as his own, he also waited until he had all the armour and reinforcements which were denied to his more skilful predecessors. Montgomery was a cautious, plodding general who had a succession of abject failures but could not be replaced as propaganda had presented him as a hero. He outnumbered Rommel 10 to 1 in tanks at Alamein yet could not catch him before Tunis, where a much better general (Patton) boxed him in.
Strangely, all three British generals mentioned were born in Ireland within a few miles of each other.
Montgomery went on to fail at Sicily and at Caen and be rescued by Patton again. His execution of Market Garden is an example of military lunacy, many died for his ego.
Both Churchill and Montgomery hated Dorman Smith who was regarded as the most brilliant general staff officer of his time, but had the nasty habit of not bowing down to Churchill. He later was hounded out of the British Army, returned to Ireland, changed his name to O'Gowan (Irish for Smith), joined the IRA and advised on their campaign in the 1950's.
What a strange world!!!!