Your own selection of quotes contradicts the points you are trying to make. Your second quotation, beyond the bit you bolded, states:Anti-Slavery sentiment in both nations has been seriously over-stated, particularly concerning the UK, but the general trend of scholarship has been to refute that since roughly the 1960s. To quote Jones again, from his Chapter Requiem for Napoleon—and Intervention -
Yet Kenner’s secret mission was anything but secret. Reports about it appeared in the Richmond Enquirer and Sentinel in late December 1864. Seward notified the Union embassy in London of the mission on January 10, and the news appeared in the Paris press on March 2. Kenner had left Richmond in disguise on January 18, 1865, lamenting that he would have had a better chance in early 1863, when both England and France were well aware of the Confederacy’s diminishing resources and the battles at Gettysburg and Vicksburg had not yet occurred. “I would have succeeded” in securing a £15 million loan when “slavery was the bone of contention.”Now, neither Napoleon nor Palmerston showed interest in the proposal. To Kenner and Mason, the emperor explained that he refused to move without England and that he “had never taken [slavery] into consideration” regarding recognition. On March 14, 1865, Mason met with Palmerston for more than an hour at Cambridge House, where the prime minister also rejected the plan, insisting that slavery was not the obstacle to intervention; the Confederacy had not proven its independence on the battlefield. The Richmond Dispatch glumly noted, “No one would receive us as a gift." The responses should not have surprised the Confederacy. Napoleon’s reply contained nothing different from his initial determination to follow the British lead. Palmerston’s argument against recognition correlated with his long conversation with De Leon in the summer of 1862. On neither side of the English Channel did slavery emerge as the critical consideration.
Rather than society being uniformly in favor of the Union, it was actually more divided with the labor classes being Pro-Confederate:
During the American Civil War, Great Britain contemplated courses of action they could take to influence the war, whether for economic reasons or diplomatic. British public opinion on what actions to take were divided (Campbell). There were a multitude of pro-Confederate groups due to the similarities the Confederates had with British society. The aristocrats and the working class of British society supported The Confederacy. However, there were also many pro Northern groups. The support for The Union in Great Britain came from the radical lower class, anti-slavery groups, as well as industrial workers. Despite the majority of British citizens taking sides, a minority chose to remain neutral because they distrusted, disliked, or just simply wished for Great Britain to stay out of other country’s domestic affairs.We also see this in response to the Emancipation Proclamation by the British Press. To quote Jones again:
News of the Emancipation Proclamation infuriated the British and the French. From Washington, Stuart indignantly informed Russell that Lincoln had enacted an antislavery decree in areas where the Union had no “de facto jurisdiction.” The purpose of the measure was to “render intervention impossible.” It bore no “pretext of humanity” and was “cold, vindictive, and entirely political.” The president sought only to offer “direct encouragement to servile Insurrections.” His action had angered Confederate lawmakers who mouthed “threats of raising the Black Flag and other measures of retaliation.” Bring in the French guillotine, declared a northern governor. If Lincoln and his Republican Party remained in control, Stuart warned, “we may see reenacted some of the worst excesses of the French Revolution.” Hammond joined Cobden in fearing the worst. To block the Confederacy’s quest for nationhood, Cobden moaned, the Union would “half ruin itself in the process of wholly ruining the South.” The use of blacks in the war effort would cause “one of the most bloody and horrible episodes in history.” The French concurred, complaining to London that the danger of a slave rebellion provided another reason for a joint intervention to end the war. A few days later, Stuart wrote Russell with no hint of dissatisfaction that Lincoln’s Proclamation seemed to be causing many in the Union armies and the Border States to desert to the Confederacy.The British press launched a blistering attack on the decree. The Times bitterly ridiculed Lincoln for considering himself “a sort of moral American Pope.” Taking advantage of the war, he sought to stir up a slave uprising during which the blacks would “murder the families of their masters” while they were away at war. “Where he has no power Mr. Lincoln will set the negroes free; where he retains power he will consider them as slaves.” His seemingly moral pronouncement was “more like a Chinaman beating his two swords together to frighten his enemy than like an earnest man pressing on his cause.” Though it supported the Union, the Spectator of London found the Proclamation exasperating. “The principle is not that a human being cannot justly own another, but that he cannot own him unless he is loyal to the United States.” London’s Bee-Hive, sympathetic to the Confederacy until the paper changed editors in January 1863, accused Lincoln of refusing to take action against slavery in the Border States in which he had authority and attempting to end the institution in the Confederacy where he did not. The Times bitterly asked whether “the reign of the last president [was] to go out amid horrible massacres of white women and children, to be followed by the extermination of the black race in the South? Is Lincoln yet a name not known to us as it will be known to posterity, and is it ultimately to be classed among that catalogue of monsters, the wholesale assassins and butchers of their kind?” Blackwood’s Edinburgh Magazine renounced the Proclamation as “monstrous, reckless, devilish.” To defeat the Confederacy, the Union “would league itself with Beelzebub, and seek to make a hell of half a continent.”
Finally:
Within a couple of weeks, the news of Antietam reached England, where the ministry initially believed the premature accounts of Confederate victory and resumed its interest in a mediation to stop the blood fest. The Earl of Shaftesbury, Lady Palmerston’s son-in-law and of considerable influence in ministerial circles, had visited Paris a few days before the battlefield news had reached the Continent and, according to Slidell, assured French officials of imminent British intervention. From the outbreak of the war, Shaftesbury told Slidell, he had supported the South’s struggle for independence against the Union’s quest for empire. He had been nearly alone in that stand, for his associates had defined the issue as slavery versus freedom. But British public opinion had undergone a revolution in feeling. Lincoln’s recent speech to the black delegation from New York and his published letter on slavery to Horace Greeley had alienated those English people calling for abolition. They now believed it more beneficial to black liberation if the Confederacy became independent.I know I'm quoting a lot from Jones, but that's just because that is what is handy to me. Support for Secession: Lancashire and the American Civil War by Mary Ellison is another good read on the subject, and demonstrates there was broad Pro-Confederate sympathy in the contemporary British society, especially among the Mill Workers and the like that are often claimed to have been Pro-Union. Case in point by Ellison is that, in 1864, Seward was presented with a petition signed by 350,000 British workers calling for the end of the conflict and the independence of the Confederacy. Other sources available are The Roebuck Motion and the Issue of British Recognition of the Confederate States of America by Lindsay Braun as well as Pro-Confederate Sympathy in the British Parliament by Davis D. Joyce.
However, there were also many pro Northern groups. The support for The Union in Great Britain came from the radical lower class, anti-slavery groups, as well as industrial workers. Despite the majority of British citizens taking sides, a minority chose to remain neutral because they distrusted, disliked, or just simply wished for Great Britain to stay out of other country’s domestic affairs.
This is a point against a British intervention in the American Civil War, not for it.