It's about William Wilberforce (Ioan Gruffud), a late-1700s British merchant's son who campaigns for years in the House of Commons to abolish slavery. He's about the same age as, and a good friend of, the prime minister, William Pitt the Younger (Benedict Cumberbatch).
The title "Amazing Grace" is about a song written by a born again slave ship captain who is haunted by the souls of the 20,000 slaves that died on his ships, John Newton (Albert Finney).
The NY Times review was about right, I think.
There are many, many excellent British actors in the movie. I recommend it.