The British got locked in a slugging match for Caen while the more mobile American forces pushed south and then swung east towards Paris. Veterans of the desert war found the close, broken country, riddled with ditches and thick hedgerows claustrophic and intimidating, while the Americans were able to develop a natural flair for a war of manoeuvre. Historians still disagree whether that was the original plan or just the way the battle developed.
The British commander of the invasion ground forces, General Bernard Montgomery (he was not promoted to Field Marshal until 1 September), was severely criticised for not taking a more aggressive role. Montgomery could justly claim to have drawn in strong forces which facilitated the American break-out, but that may not have been his original aim.
It is possible he hoped to fight the mobile battle east of Caen with the British armour from Lt-Gen Miles Dempsey's Second Army, while the American First Army under Lt-Gen Omar Bradley got on with the mundane business of securing the ports of Cherbourg and Brest. It may have been lucky for the Allies that a different plan was forced on him.
By 10 June, the separate D-Day beachheads had been linked and the Americans were attacking inland towards Cherbourg, while the British were preparing to take Caen. Initially the US forces in the west encountered terrain which was more difficult than that facing the British to the east.
But despite heavy bombardment of Caen and of the German positions to the south, the British attempt to outflank the city at Villers-Bocage, to the west on 10-12 June failed, as did another attempt to the west by 15th Scottish Division from 24 June to 1 July.
A third British and Canadian attempt to capture Caen from 18-20 June, Operation Goodwood, which tried to cut behind it to the east using a strong armoured force, also failed. The US forces, meanwhile, occupied the Cotentin peninsula and forced Cherbourg to surrender on 27 June.
The argument about Montgomery's original plan has raged since the end of the war. Brigadier Kenneth McLean, a senior planner, said that 'for Montgomery to say he was holding the Germans so Bradley could break out was absolute rubbish and a complete fabrication that only developed after he was stopped outside Caen'.
Montgomery later said his forces were short of ammunition and troops. He said: 'At best it would have been touch and go whether we could take it or not . . . the British Army was a wasting asset. The War Office told me before D-Day that it could guarantee reinforcements only for the first month. It would have been very easy for me to yield to public criticism and American pressure and to have made greater efforts to gain ground on this flank.'
Manpower was a constant concern. By early July the British were seriously short of trained infantry, as their casualties had been heavier and those among other units lighter than expected.
It seems that Montgomery was sensible to proceed as he did, maintaining constant pressure on Caen to draw the Germans in while Bradley prepared to attack in the west. But at the end of June the Americans, too, were stuck in the difficult terrain.
But the Americans solved the problem with a device improvised from the obstacles the Germans had scattered on the beaches. The steel stakes were sharpened and fitted to the front of hundreds of US tanks, enabling them to gouge their way through the hedgerows. It was an example of the flexibility that characterised the well- equipped US forces.
Little by little the Germans were forced back until on 17 July Bradley's Army was formed up on the line Lessay-Periers-St Lo. On 25 July, the Americans launched Operation Cobra, breaking through west of St Lo.
It was unexpectedly successful because most of the German forces had been drawn east to Caen. Only one Panzer division, the Lehr, was in the area to attempt to block the attack. The heavy air bombardment also helped, but not until after one of the worst 'friendly fire' incidents of the war in which planes from the Eighth Air Force dropped bombs short, killing 111 Americans including a general.
Finding resistance weaker than expected, the US forces advanced rapidly. The American Third Army, under Lt-Gen George Patton, the most flamboyant US commander of the war, turned west towards Brest, to fulfil the plan to capture the port.
But on 4 August, Montgomery issued the first change to the original plan. Patton was to swing eastwards in a wide-reaching attack across the rear of the German armies. It may not have been the original scheme but Montgomery deserves some credit for exploiting success and the particular qualities of Patton and the American forces. The British and the Canadians were to continue attacking southwards towards Caen.
The Germans tried to cut off the advancing Americans by attacking west from Mortain but the Allies intercepted their coded transmissions and defeated them on 6 August. This had drawn German armour from Caen, which in turn allowed the British and Canadians to push south.
The mobile US forces then swept round the Germans to trap 50,000 of them in the so-called 'Falaise pocket'. The Canadians reached Falaise on 15 August and the US XV Corps had reached Argentan two days earlier.
But despite efforts to seal the pocket, by now only 15 miles wide, the majority of the German forces escaped across the Seine by ferry and temporary bridges. The pocket was finally closed on 20 August, the Allies inflicting fearful destruction with artillery and aircraft, including rocket-armed Typhoon fighter bombers.
Modern US military analysts have criticised the Allies for not attempting a bigger encirclement all the way to the Seine. But Patton stopped his encircling spearheads at Argentan to wait for the slower British and Canadians.
The British official history describes the British left flank as 'the pivot on which the main stroke would hinge. It must always remain secure or the whole movement might lose its balance'.
That was not the original plan, nor is it correct to view the British and Canadians as locked in a static battle while the Americans did all the manoeuvre. When the Americans drew in German forces, the British and Canadians advanced.
Fighting together in north-west Europe for the first time in the era of mechanised warfare, the British and US forces were each finding their feet. As Churchill noticed, the Americans displayed a remarkable ability to adapt.
Patton, audacious to the core, converted the local breakthrough by the First Army into a theatre- wide break-out that only ground to a halt in September because of fuel shortages.
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