NO attempt to tell the story of D-Day and the battle for Normandy is complete without mention of the denouement: the Battle of Falaise.

As we told on previous days, the Allies had landed on the beaches on D-Day at the beginning of June. They had pushed through the orchards and the fields of Normandy, overcoming bloody and brutal resistance. By early August, they had the Germans on the back foot.

The Canadians and the Poles were heading south; the British were moving in from the south-west; the Americans were covering vast amounts of territory each day and were now swinging north. The Germans found themselves trapped near the small town of Falaise, the noose tightening around their necks as the "Falaise pocket" closed about them.

General Sir Bernard Montgomery, commander of the British forces, said: "This is an opportunity that comes to a commander not more than once in a century. We are about to destroy an entire German army."

Every night for about a week, the RAF sent more than 1,000 planes to bomb the German soldiers. Adolf Hitler, back in Berlin, demanded that his men should attack; the Allies made further landings on the French coast and attacked along the Mediterranean; Field Marshal Gunther von Kluge, Hitler's leader in Normandy, disappeared - apparently all German radios were down.

Hitler later said that this day - August 15, D-Day+70 - was the worst day of his life.

Fearing von Kluge was negotiating a surrender, Hitler sent Field Marshal Walther Model to Normandy to take charge. Von Kluge reappeared and, seeing what was happening, committed suicide with the help of a cyanide pill.

The noose tightening, the German soldiers began streaming backwards along the two roads out of the Falaise pocket. Their vehicles were four abreast as Allied airplanes picked them off - the stench of death was said to be so strong that it reached the fighter pilots 1,000ft up.

The Battle of Falaise finished on August 21. The battle for Normandy, begun on the beaches 76 days earlier, was over.

In another four days, Paris would be liberated.

At Falaise, 10,000 Germans were killed and 50,000 were taken prisoner. The scenes of carnage made indelible impressions even upon the most battle-hardened of soldiers.

General Dwight D Eisenhower, leader of the US troops, said: "Forty-eight hours after the closing of the gap, I was conducted through it on foot, to encounter scenes that could only be described by Dante. It was literally possible to walk for hundreds of yards at a time, stepping on nothing but dead and decaying flesh."

Some historians believe that the Allied commanders bottled it, saying that they could have closed the gap earlier and allowed too many Germans to escape.

Members of the 6th Battalion of the Durham Light Infantry arrived a couple of days after the slaughter but before the mopping up operation had begun.

One veteran speaks of, almost as a dare, touching the body of a German who was still at the wheel of his burnt-out car. It crumbled to ashes on his fingertips.

Ernie Harvey, from Hetton-le-Hole, remembers "terrific carnage". He says: "There were Germans scattered all over the fields with no clothes on. A vehicle had come off the road into a tree and I opened the door and the dead driver fell on top of me. My mates screamed 'let him go, let him go' and he crashed out like a ton of bricks."

His DLI colleague, Ken Lodge, from Pelton, remembers a German officer lying on his car bonnet. "There was a massive hole through his skull. I could see right through - his brain had been cleaned out."

It was these scenes that stayed with these soldiers in later life.

"For six months after, you still had the smell of death in your nostrils," says Ernie.

Years after, they came back to him in dreams. "My dad would say 'you were shooting again last night'," recalls the 80-year-old grandfather.

For Ken, it was the rain that brought it back. "Every time it rained, I could smell cordite," he says. "It tends to hang when it rains - especially by hedgerows."

Since D-Day, in round figures, 21,000 Americans had been killed. About 95,000 were wounded and 10,000 were missing.

The British and Canadians had had 16,000 killed, 58,000 wounded and 9,000 were missing.

About 14,000 French civilians had been killed, and the German dead numbered anywhere between 50,000 and 65,000.

When Paris was liberated on August 25 - D+80 - Operation Overlord, which had begun on D-Day, was hailed an immense success. And it was. Although there were still many battles to go, Europe was being liberated from an appalling evil.

But what a cost.