October and November mark the 100th anniversary of the 1st Battle of Ypres, when Falkenhayn sent most of the remaining reserve units available to the German Army on a drive to the Channel ports, primarily right through the BEF. As recorded by Anthony Farrar-Hockley in his book "Death of an Army", the BEF that redeployed in Flanders from the Aisne front had made up most of the crippling losses from Mons, Le Cateau, and the Aisne through the recall of reservists and the arrival of active units from the far-flung reaches of the Empire. These replacements, along with the arrival of the Indian Corps, gave the British a stronger force on paper than the original 5-division BEF, although unit cohesion was still an issue for battalions that had been fighting since late August and were dealing with significant turnover in personnel.
By the end of the Ypres fighting in late November, just about most of the battalions in the BEF had been reduced to cadre strength, with the most serious losses falling on the field officers and NCOs who both the most dynamic leaders and the foundation for the future Army. Coming on the heals of the earlier losses, this meant that the professional British Army had essentially ceased to exist as a coherent force.From this point on the fighting would be done by territorials and Kitchener's volunteers, supported and directed by a leavening of prewar professionals.
Given this impact, which would affect the British Army both in WW1 and WW2, shouldn't history rate Falkenhayn's offensive as a strategic success, despite the failure to take the Channel ports? Deploying the reserve corps elsewhere, say against the Russians or the French, would not have offered any decisive opportunities, and it would have left the British with a core, professional force able to conduct far more effective offensive operations in 1915 and 1916.
I don't agree ith the assessment that the BA had "...essentially ceased to exist as a coherent force"; you are equating the BEF with the entire BA which it wasn't. More importantly, I don't see how the pre-war Regulars would have been able to "...conduct far more effective offensive operations in 1915 and 1916". The presence of more pre-war Regulars wouldn't have prevented the shell shortage of 1915 or been able to cope with the tactical constraints & conditions prevailing at Loos etc, and they would not have been able to provide the numbers for the Somme, so you'd still have been dependent on Kitchener's New Armies in any case.
I agree it's debatable whether the BEF would have been able to fight with more success in 1915 given the shell and gun shortage, but at the same time there is no question that it helps to have professional, experienced soldiers available to train and lead territorials and new recruits. Did a little bit of background reading and came up with some basic numbers, although there is some disagreement/inconsistency.
Casualties - Sources seem to agree that the British suffered ~90,000 to 100,000 casualties in 1914, almost all of which were incurred by the active Army and the replacements that reached the BEF from the Reserve. Given that the BEF lost no major units to encirclement and capture, nor was it's defensive line ever broken to the point that the Germans overran rear areas, the majority of those casualties would have been among the infantry, probably on the order of 70,000 to 80,000. In addition, ~26,000 were evacuated back to Britain due to illness.
British Army Strength in 1914 - According to one source, the British Army in 1914 had an active complement of 247,000 men, with approximately 160,000 in the infantry, spread among 157 battalions. According to another, the 1914 Infantry establishment was 134,000 men, with an actual strength of 126,000. For the time being, let's stick with the number of 126,000. The Army Reserve totaled 145,000 men who were liable to be called up upon mobilization. I don't know what fraction were infantry. The total number of Special Reserve troops was established at 77,000 but there was an actual strength of 61,000, with almost all of the shortfall in the infantry arm. Similarly, the Territorial Army had an establishment of 303,000 but only had a strength of 258,000, again with the shortfall in the infantry. Neither the Special Reserve nor Territorial Army played a major role in 1914.
Components in 1914 Fighting - If, as with the rest of the Army, the Army Reserve had more than half of its strength in infantry, one can guess ~80,000 infantry available upon mobilization, and since these would presumably be available in Great Britain, than the BEF should have been backed up by a reserve of nearly 100% in infantry. However, reports from the time indicate that units absorbed almost all of their reserve soldiers in order to come up to war establishment. The same source that cites a prewar active infantry strength of 126,000 men indicates that more than 50% of the infantry in the 1914 BEF came from the reserve. I suspect that number may represent the total across the entire year after casualties and replacements are taken into account. Nonetheless, it seems that the BEF's active battalions were significantly understrength at the time war broke out, more than the 126,000 strength vs. 134,000 establishment figures would indicate.
Impact on the Army - The bottom line is that the "professional" infantry available to the British Army in 1914 was a total of 126,000 active and some fraction of 145,000 in the Army Reserve. I will assume ~50% as 75,000, giving a total of ~200,000. Of these ~80,000 became casualties, and as a rough estimate ~15,000 were invalided home due to illness. Consequently, on average the infantry had been reduced by something on the order of 50% relative to the entire army. Most of this impact would have been on the "home" battalions, with those on overseas service suffering their share in 1915 on the western front and in Gallipoli. As in other wars, these losses would have fallen disproportionately on the officers and NCOs, the men who were most needed to build the mass army Britain needed for the war effort. An example of this shortage is illustrated by the experience of Winston Churchill, who had seen active service in the cavalry in the 1890s and spent time with the Yeomanry in the decades before the war. With only a short amount of seasoning in the nature of trench warfare, he was assigned to command an infantry battalion in 1915, where he was known for many good qualities but also a near complete inability to give proper commands to the men, calling out incomprehensible cavalry commands during combat. Politics aside, men like Churchill were thrust into their positions because there weren't anything like enough experienced infantry officers to go around. Most of them were dead, wounded or captured at Mons, Le Cateau, or Ypres.