I've never seen the movie myself, however, after searching on www.imdb.com I found out it's called "Legend", directed by Ridley Scott, starring Tom Cruise and Tim Curry.
I'm sorry, have I been living under a rock forever? Why haven't I heard of this film directed by this great director, starring two great actors, ABOUT UNICORNS?!? Maybe it didn't do too well in the UK, anyone know?
"Legend" didn't do that well, but turns up on TV from time to time. I love the film, and would recommend the Region 1 "Ultimate Edition" DVD, which has the US cut (Tangerine Dream score) and the European cut (Jerry Goldsmith score). There's a great site for Legend info here: http://www.figmentfly.com/legend/index.shtml
I don't remember there being a 'fire' phrase in Legend..but i think i fell asleep during it. I do remember a film which was serialised as part of the Tales of Europe programme shown on TV called 'The Singing Ringing Tree'. It featured a unicorn, a princess, a bear, a giant fish and a wicked dwarf who could fly. He cast various spells one of which was to put a ring of fire around things to stop the princess undoing his spells...but i don't know if he used that phrase.
Does any one remember more clearly?
cobweb, "Fire, fire burning higher" was definitely from "Legend" - Blix (the goblin) says it when experimenting with the powers of the unicorn's horn. As for "The Singing Ringing Tree", it got into the lower rungs of C4's Top 100 Scary TV/Film moments recently and was #20 in a Radio Times Poll of Scary shows! Anyway, there's a fan page here: http://uk.geocities.com/singringtree/
and it's available on DVD and VHS.