Oh boy, that's a complex one. 'Effective'? You could argue that the Spanish forces in the Peninsular were more effective than any British force, because both their regular armies and irregular forces tied up and killed more French combatants than the British. However, I will narrow this down to what seems to be at the heart of your question; why did the British line infantry acquire the reputation ascribed to it by General Soult and General Reille?
For reference, I did my undergraduate dissertation on Wellington's army in the Peninsular. While researching this, I was taught by a PhD student working on the British Army in the Low Countries. These could perhaps represent the respective high and low points of the British Army during the Napoleonic era. To allow the Low Countries campaigns in, we'll stretch that from 1793 to 1815.
I refuse to use a TL;DR, but the brief explanation is that Soult and Reille's opinion were biased, and founded on experience against the well-funded, well-supplied, and well-led Allied forces in Spain. I have little doubt that Joseph Souham might not have had quite so impenetrable an opinion of them. However, within this, there does seem to be evidence that British troops were, on average, more experienced and more resolute than some of their continental counterparts. I am British myself, so please forgive me if I consistently adjust too far against this view, but from my research into the military training of British troops of the line, several advantages can be found.
For one thing, the British connection to saltpetre mines in India meant that gunpowder was less expensive to the army, and thereby live-firing drills were more common. Recruits could get used to the smoke and smell of large-scale firearms discharges, and thereby be more accustomed to it in the heat of battle. A newly recruited line infantry might get as much as six months training, but a militiaman brought up from the militia scheme might be moved out in less than two, depending on need.
A second major point is the British combat doctrine that became codified in the Peninsular campaign. The counter-charge seems to have been a highly effective tactic, most especially on the defence. At Vimeiro, Talavera, and Waterloo, to name three examples, counter-charges by British infantry in a defensive position were decisive in driving back large attacks. This consisted of waiting until the enemy were at extremely close range, sometimes as little as twenty yards, and then pouring a huge volley into them - then giving three cheers, and charging. This required not only a certainty that the enemy were GOING to advance, but also a very strong sense of discipline. When properly executed, the tactic was highly devastated.
However, many battles, such as Barrosa, Fuentes Des Onoros, Salamanca, and Vittoria, were either offensive in nature or saw the French columns (as they preferred to do) deploy into line and begin an exchange of musketry with their opposition. It seems the training of the British troops and their willingness to deploy into two-deep lines rather than three paid off in this regard, as these exchanges were almost always won by the British. I am unwilling to attribute this to 'better men, better soldiers', but I would note that the cream of the British Army was used in the Peninsular, while the French had a very larger army, and thereby a far higher chance of meeting a formation with less experience. However, we do find that when experienced and motivated troops went up against British troops in such a shooting match, such as at Albuera, the British managed to overcome them; if barely.
I would very much like to provide a contrast to this; the deplorable treatment of civilians by British troops not only at Badajoz and Ciudad Rodrigo, but on the retreat to Corunna, and in the Low Countries campaigns. The behaviour of these men towards people they were sent to save might be understandable under the circumstances, but it should nevertheless be shamed and noted as a black spot on the reputation of the British Army in this time period. Hence why some of Wellington's more colourful remarks about his troops were not ill-based.
Do I think the British Army performed well across the entirety of the period? No. Their performance in the Low Countries was abysmal. But I do find that their major disadvantages were formulated around incompetent officers and poorly planned offensives. Soult's experience against the British infantry was significant, and his beliefs founded in solid facts. You may find another quote concerning the British and Portuguese troops interesting. Written after the bloody Battle of Albuera in 1811, Soult noted -
"There is no beating these troops, in spite of their generals. I always thought they were bad soldiers, now I am sure of it. I had turned their right, pierced their centre and everywhere victory was mine – but they did not know how to run!"
It is fair to argue that the British Army had a mixed record during the whole era, but in the Peninsular and at Waterloo, the infantry were steadfast, determined, and few in number.