Int he film 'Belle' the main protagonists are vehemently against the slave trade and refer to it as being inhumane whilst also stating that it is a source of significant portion of the countries revenue. This indicates that the trade was once, at least, more socially acceptable than during the time period protrayed.
Is it true that the slave trade was more socially acceptable when it was established and if so what were the social or cultural changes that eventually led to it becoming contraversial and eventually outlawed?
Was it a gradual change or did it happen rapidly - was religion involved and if so what particular to English society made it happen sooner there than other European powers?
It was indeed a gradual change.
There are several reasons for the slow change towards a strong opposition to slavery.
Slavery was more or less considered a decent institution to be forced upon "others", those of a different race or religion. While slave-like conditions were sometimes forced upon indentured servants and convicts sent to the colonies, it was not true slavery, especially as the children of such people did not inherit their status, and they still had the right of ownership and to keep what was theirs, whcih slaves did not.
For the later part of the 1600s and the early 1700s, the planter elite made huge amounts of money off of sugar, tobacco and cotton, with the first being the most prominent, using slave labour. The money they made and the system of rotten boroughs in Britain (where the parliament seats were not updated with population changes, meaning that in some places 30 votes could be enough for a parliament seat, an easy group of people to bribe) meant that they held a substantial amount of power.
However, towards the end of the 18th century several things had happened that started to change this. There were no provisions for slavery in English law, and on several occasions slaves were freed when in England, with the Somersett's case of 1772 as one of the most famous, where the judge, Lord Mansfeld declared that slavery was illegal in Britain with the motivation that "the air of England is too pure for any slave to breathe".
As it had been established that there were no base in common law for slavery, and that slave owners could not bring their slaves to Britain upon fear of losing their property, slave proponents started losing influence.
At this time, Britain also lost a substantial part of its colonies where slavery was widely used when the US declared its independence 1776. For some time, India, where corvee labour and cheap salaried labour was used rather than slavery had started generating higher amounts of revenue than the sugar plantations in the Carribean.
Those that benefitted from slavery lost, both in absolute numbers and relative economical power in Britain.
At the same time, the old arguments for slavery - them being infidels, heathens or pagans and speaking a different language started to become moot. Most slaves converted to christianity and learned to speak the language of their masters, English. A growing opposition among religious groups saw it as wrong to keep fellow christians enslaved.
Yes, slavery and slave trade was considered socially acceptable at the beginning of the 18th century and gradually became more and more unacceptable as the plantation owners lost economical power and lost a large part of their numbers.
I just want to add to vonadler's very informative post that for further reading you might like Bury the Chains by Adam Hoschchild, which covers much of the same territory as what is described here.