So to preface this, the "battle sequence" was not intended as a "singular" battle - but rather designed to encapsulate the "average" experience of a British soldier between 1914-1918. To paraphrase Jackson himself from the "making of" documentary that followed screenings of the film, he "realized that being shelled in 1914 wasn't all that different from being shelled in 1916 or 1918" (this is of course a rough paraphrase as I do not have the making of on hand). So what Jackson did was mold together oral histories of different battles into one "experience". Although this is one area where I disagree with his interpretation, as the battle experience of a soldier in 1914 would be wildly different from 1916 which would be different from 1918 (and even different parts of 1918).
So the big difficultly of analyzing the oral histories presented in the film is that they're mixed together, and without any real context. Experiences of different battles got melded together, and without being able to place a name to a voice. This means you can't determine the individual's unit, what battle(s) they were actually in, and really do any sort of source criticism on the oral history. Oral histories have to be treated carefully as they are often taken so far after an event, and in the case of the ones used in film, they were taken about 50 years after the war for a 26 Part BBC Documentary called The Great War. So at that point the veterans have had 50 years of life that can impact their memories and their interpretation of them.
On this topic I really like to quote from Richard Holmes's Tommy: The British Soldier on the Western Front 1914-1918.
But the interviewing of veterans in the 1970s and beyond concentrated, as it had to, on those who had survived. Like accounts written long after the events they describe, interviews with survivors inevitably reflect the past through the prism of the present. [...] Sometimes survivors played their roles too well [...] And sometimes, just sometimes, they tell us this because they have it heart it themselves.
So we should be extra cautious about how we use and interpret oral history and other non-contemporary evidence. It is often far too late-recorded oral history; occasionally forgotten voices tell us about imaginary incidents. Much better to go back to what people thought at the time.
With that out of the way, the specific quote you mention I think may be this one:
Our captain was a splendid man. He would never bark an order at you, he would give an order in a conversational way. [Here he is quoting or paraphrasing an order given] 'We don't know exactly how far this trench is, but it's between 200 and 300 yards. I will go over in the first wave and you'll be in the second wave. And as soon as the curtain fire starts we move. Now go on and tell your men to be ready' [End quote] and this is the sort of order we got.
So while we can't say for certain what battle he was in, his quote can give us some likely clues. First is the use of "waves". In this context they wouldn't be unorganized "human waves" as popular culture would usually have you believe. Paths of Glory for instance is far off the mark, as is All Quiet on the Western Front. These films show a large, unorganized mass of men rushing the enemy trenches, only to be mowed down and pushed back by Machine-gun fire. The "waves" mentioned would not be like that. And depending on the battle and the unit these "waves" would and could take on different forms.
If it's an earlier battle it may have looked something like this (Paddy Griffith; Battle Tactics of the Western Front: The British Art of Attack 1916-18; page 54)
Within the 9th Scottish Division, for example, the attack at Loos was made by four battalions in line on a frontage of 1,600 yards, with each battalion split into three waves, one behind the other. Behind each battalion followed a second one in the same formation, ready to leapfrog through; and behind that came a whole brigade in general reserve. The depth of the attack at any given place was therefore at least six lines of men, at intervals of perhaps two yards between each man. Some variant of this layout, albeit thinner and shallower in later years, would remain standard practice for most of the war, particularly in the battle of the Somme.
So that is about 800 men per 1600 yards (4800 feet). Each man spaced at about 2 yards (6 feet) apart. Without having the 9th Scottish Division's history in front of me I can't say how the attack was divided up between each battalion of the division, but I'd say it's likely that each battalion covered 400 yards. So that's about 200 men from each battalion in each line.
Next Griffith mentions that
At Longueval on 14 July 1916, for example, the same division [9th Scottish] attacked again with four battalions in the front line, but this time with each company in a column of platoons, making four successive platoon waves with seventy yards between them. In 26th Brigade each battalion had a frontage of two companies, with the remaining two in second line, and a second battalion following behind, to give a total depth of sixteen platoon waves attacking any given section of front. In 27th Brigade, by contrast, each battalion had all four companies in the front line, making just four waves, and only one battalion backing up the two in front. Overall the division's foremost front line, with six platoons advancing side by side on a frontage of perhaps 1 ,000 yards, represented a density of about one man to every five and a half yards
Loos took place in 1915, while the following examples took place during the Battle of the Somme in 1916. There was a huge amount of change and variation in how attacks were carried out in a short amount of time. A platoon would be about 50 men organized into about four different squads. So that's groups of fifty organized men working their way towards their objective. By 1916 you start to see the introduction of grenades or "bombs" on a wider-scale than before (it started its transition from being a more specialist weapon to a generalized weapon), the usage of the Lewis gun to provide covering fire, and after July 1st, an evolution in the British usage of Artillery. All of these (and many other things I haven't mentioned) started to work in tandem to allow the soldiers on the ground to advance to, and take, their positions. They would have been, in a sense "rushing" German trenches, but it would have been backed up by decently sophisticated infantry tactics, artillery, light machine guns, aircraft, and later on in some cases, tanks.
So in short, what the veteran describes isn't really wrong - as he is describing the usage of "waves" (which did vary in size and composition depending on the battle and phase of the war), and "curtain fire". "Curtain Fire" is where the artillery essentially tries to cut off the enemy from reinforcements, supplies, and retreat by continuously bombarding specific points. This is different from say a "Creeping Barrage" which would be barrage that moves forward in a predetermined interval (both time and distance that the barrage has to move forward) in order to help cover the infantry's advance. With what he said in that quote he was likely talking about some point in the Battle of the Somme (and even then very likely the start of the battle). Curtain fire was in usage during the war, but again it depends heavily on the unit, battle, and portion of a battle that he's specifically referring to. Without more context as to who he was, more can't really be said about if what he said was accurate for his specific circumstances rather than in general.
As I alluded to earlier, all of this could all depend on local conditions, as /u/DuxBelisarius talks about this in his response about myths around "walking into machine-gun fire". As well /u/NMW talks about the more strategic and operational goals and ideas surrounding massed attacks here.
Sources and Further Reading
That was a fantastic answer.....thank you.