A huge generalisation and hard to support. While the left have been responsible for many great reforms, it is historically inaccurate to say "every progressive movement.......have all stemmed from the liberal/ socialist...side of politics."
You quote the the abolition of slavery. The long campaign was led by William Wilberforce. Even tho' he was an independent MP, his personal leaning was to the right and he was a lifelong friend and confidant of Pitt the Younger. His motlvation stemmed from religious belief, not political considerations.
Similarly, the greatest, perhaps, British reformer in the 19th century was the Earl of Shaftesbury with a hugely varied string of reforms from Factory Acts to the treatment of mental health. He was absolutely a Tory.
As for Homosexuality, you have to go back to the Spectator magazine in the early 50s for the first, and relentless, campaign for legalisation.
The editor was Iain Gilmour, a tory. That mag has a long tradition of supporting reform from a position on the radical right. See, eg, its support for the The Tolpuddle Martyrs.
Everybody wants to be associated with great social reform, but you should not swallow myths and propaganda, but rather study the facts.
And you should study my post.
I stated that the exception to the rule was the decriminalisation of homosexuality. Homosexuality, unlike grinding poverty and inherited wealth, is a state of being that pays no mind to social class or status.
You're right, Wilberforce, despite being an independent MP, was deeply conservative when it came to challenges to the existing political and social order. He advocated change in society through Christianity and improvement in morals, education and religion, he was an evangelical Christian, it was from these foundations that the campaign for the abolition of slavery was rooted. Similarly he founded the Society for the Suppression of Vice as a remedy for the rising tide of immorality.The proclamation setting the society up commanded the prosecution of those guilty of "excessive drinking, blasphemy, profane swearing and cursing, lewdness, profanation of the Lord's Day, and other dissolute, immoral, or disorderly practices".
Wilberforce's involvement in the abolition movement was motivated by a desire to put his Christian principles into action and to serve God in public life. He and other evangelicals were horrified by what they perceived was a depraved and un-Christian trade, and the greed and avarice of the owners and traders. Wilberforce sensed a call from God, writing in a journal entry in 1787 that "God Almighty has set before me two great objects, the suppression of the Slave Trade and the Reformation of Manners (moral values).
Clearly Wilberforce was no socialist, but does he stem from the liberal progressive wing of politics? I think I have to agree with you he does not. Social reform, brought about by adherence to a religion is not exactly common, but good works is, and it was a desire to do right by all gods creatures that motivated Wilberforce and that's why, in addition to his work on slavery and loose morals, he had a hand in the foundation of the RSPCA.
As for various reforms in the Victorian period, they were, for the most part, motivated by either Christian virtue, self serving philanthropy, political necessity or common sense. I would argue that none of these reforms were motivated by right wing ideology, even if their advocates might have been conservatives.
The example I use for a conundrums like this is Lyndon Johnson. Lyndon Johnson was the most progressive post war US President, the list of groundbreaking progressive policies he championed is breathtaking, yet he was not himself a progressive and pursued the Vietnam war with vigour.
Johnson's politics was informed by his experiences with the pitifully poor in his youth, hence he had a burning desire to address their condition. He was a ruthless politician, smart enough to know which way the wind was blowing, and most importantly,Vietnam notwithstanding, he had the strength to know when something just made sense.