Yes, the name "Chariots of fire" comes from a line in the hymn. By the way, it is my favorite hymn. It has the perfect combination: lyrics by an English poet (Blake), music by a Welshman (Parry), and arranged by the greatest English composer of the 20th century (Elgar).
I think the banning of "I vow to thee my country" and "Jerusalem" is outrageous. I like American patriotism and English patriotism (and also Welsh patriotism too--Wales just won the 6 nations rugby championship for the first time since 1978).
The Church of England seems neither English nore a Church.