It wasn't that they CHOSE to use shrapnel as opposed to high explosive. If anything, it was that they had TOO MUCH shrapnel, and TOO LITTLE high explosive.

This had to do with the fact that Britain had really only begun to massively expand it's armaments production in the fall of 1915, following the infamous Shell Crisis, after the Battle of Loos. Field Marshal Sir John French, the commander of the BEF who was sacked when the attack on Loos failed, let it slip to some journalists that the attack had failed because the British lacked sufficient ammunition to support the operation. Although things like German counter-attacks, mixed results of British gas attacks, and French's decision to keep the British reserves too far back to speedily exploit a breakthrough/break-in, were also reasons for the failure, he was justified in singling out the ammunition shortages. The result of the scandal was that the Asquith Liberal Government fell, and was forced to form a coalition government. A Ministry of Munitions was created under David Lloyd-George's leadership, which was charged with expanding and increasing the production of war materials.

They were successful in this, at least on the surface. Ammunition and weapons production increased massively from the winter of 1915 onwards. Unfortunately, due to inexperience, labour shortages, and the pressure to deliver adequate quantities of materiel, corners were, perhaps inevitably, cut. Quality control steps were reduced or rushed, and existing assembly lines churned out the Shrapnel shells that WERE being produced, rather than accept the delay that would result from re-tooling lines to manufacture HE. The aim was for quantity, at the expense of quality, while British Industry was kicking into high gear.

Here's a quote from Brig. Gen. James Edmonds "Military Operations France And Belgium" (1931), to illustrate the above point:

"Despite improvisation and inexperience, in 1916 British war industry produced 33,507 machine-guns, 5,192 trench mortars with 6,500,000 rounds, 127,000 long tons (129,000,000 kg) of explosives and 84,000 long tons (85,000,000 kg) of propellants. Mills bomb production rose to 1,400,000 per week and the output of shells rose from 4,336,800 in the first quarter of 1916 to 20,888,400 in the final quarter, for an annual total of more than fifty million. 148,000 long tons (150,000,000 kg) of ammunition were expended on the Somme from 24 June – 23 July and 101,771 long tons (103,404,000 kg) were landed in France. Heavy guns and howitzers burst on firing, due to defective shells made from inferior steel, which had hairline cracks, through which the propellant discharge detonated the shell. 8-inch howitzer fuzes failed so often, that the battlefield was littered with duds and an attempted remedy made the fuzes fall out. Many shells failed to explode, due to deterioration of the explosive filling; defective fuzes in all heavy guns caused premature detonations, while many guns misfired due to poor quality barrels. 60-pounder guns averaged a premature every 500 shrapnel rounds and 4.5-inch howitzer shells exploded in the barrel or 4–5 yards (3.7–4.6 m) beyond the muzzle, the crews becoming known as "suicide clubs". Some propellants were not fully consumed on firing, requiring the barrel to be cleaned after each shot, which slowed the rate of fire. Some copper driving bands on 18-pounder field gun shells were too hard, which reduced the accuracy of the gun; when H.E. ammunition was introduced late in 1915, premature detonations and bulges occurred, with a burst barrel every thousand shots. There was a shortage of buffer springs, replacements were sometimes worse than worn ones and spare parts for every mechanical device in the army were lacking. Some shells exuded explosive in the summer heat, flare fillings decomposed, phosphorus bombs went off spontaneously, the firing mechanism of the heavy trench mortars failed on 1 July, Stokes mortar ammunition was chronically unreliable until replaced by improved designs, many Mills bombs went off early, rifle grenades were either premature detonations or duds and a make of rifle cartridge jammed after firing and had to be scrapped."

On top of this, the majority of the artillery that carried out the Somme bombardment, were still field guns, with a still insufficient number of medium & heavy howitzers, to really hammer the German dug-outs. More over, north of the Albert-Bapaume road, the artillery was directed to shell the German first and second defence lines, which meant that the weight of the artillery fire was spread between the two positions, rather than focused on the first. I say "north of the Albert-Bapaume road", because that is where the British were mauled. SOUTH of the road, the German defences were not as strong, while the British positions gave artillery observers a better view of the German lines, which, combined with aerial reconnaissance, made the artillery here more effective. Here as well, only the German first line was the objective, and so the artillery preparation was comparatively much stronger.

In the end, the key to the varied results on the first day was the enemy: the northern part of the line, incidentally, is where the Germans concentrated their reserves, and strengthened their defences the most. Combined with German artillery and machine gun fire, the fighting north of the Albert-Bapaume road would have been extremely bloody, whether or not British units were able to take the first line of trenches. Some, like the 36th Ulster Division, did just that at the Schwaben Redoubt, but they failed to clear the positions behind them, and so were attacked from all sides, as well as shelled by German artillery.

If you're interested in further reading:

Mud, Blood and Poppycock (Gordon Corrigan) The Great War: A Combat History of the First World War (Peter Hart) Three Armies on the Somme (William Philpot) War of Attrition: Fighting the First World War (William Philpot) Through German Eyes: The British & The Somme (Christopher Duffy) The Somme (Robin Prior & Trevor Wilson)

Hope that helps! TL;DR: too much shrapnel, not enough HE; the Tommies gave it their all regardless.