Well, yes, it is a lot more complicated if you want to get into all the details. However, the concrete political movements that led to the abolition of British slave trade in 1807, the subsequent British commitment to stamp out the slave trade globally with the Royal Navy, the Empire-wide Abolition Act in 1833, and the American struggles over slavery that culminated with the Civil War, were overwhelmingly instigated and promoted by religiously motivated people coming mostly from Quaker and certain other Dissenter groups. The modern anti-slavery attitudes draw their ideological origins primarily from these people and their work.
Also, some of your details are not quite right. Locke was by no means a principled opponent of slavery -- he considered slavery legitimate in certain cases ("state of war continued") that he outlined in his Second Treatise. (Also, I have read, though never seen conclusive evidence, that he had some financial interest in the slavery business and participated in drafting a strongly pro-slavery constitution for the Carolina colony.) Mill can't be classified under the Enlightenment unless its definition is made absurdly overbroad, and even regardless, he was a latecomer to the whole issue.
It is true that the British and American Enlightenment was never as atheistic as the French. (This was to some degree because of its representatives' actual beliefs, but also because atheism was more dangerous for one's reputation and career in Britain and America than in France.) However, the leading British and American Enlightenment figures -- from Locke to Hume to Smith to Gibbon to the U.S. founders -- were definitely not among the leading anti-slavery activists of their day, and I'm not sure if any of them even made a principled condemnation of it. Whatever we make out of it, the people who actually started and promoted abolitionism as an ideological and political force were first and foremost religious Quakers and other Dissenters, for whom the Enlightenment was at most a side influence.
I wanted to bring attention to two posts from Razib Khan's Discover magazine gene expression blog (some of you may have been readers of the still active original gnxp) on the polemic surrounding Pinker's The Better Angels of Our Nature.
Relative Angels and absolute Demons (and the related But peace does reign! )
I generally agree with some of his arguments, but found this quote especially as summing up some of my own sentiments: