If the tiles are blackened from soot and char, some baking soda and a toothbrush might work. Toothpaste is a good fine abrasive as well.
The process would be to get as much char off as possible with a razor blade scraper (being careful not to scratch the tiles). If the tiles have a raised design you might not be able to do much with a blade. You can also try scrubbing with a green pad. Then try the baking soda or toothpaste with a tooth brush.
If you don't mind the fumes, then oven cleaner will work, too. Test first to make sure it doesn't discolor the tiles (it shouldn't, but you never know...)
If the tiles are old and have crazing (fine cracks) then the soot might be worked in them and that won't come out. Just consider that the patina of age and don't let it worry you.
Just a word of warning.
On most Victorian and similar tiled fireplace inserts the tiles are just clipped in place or in slots.
They are not very well supported on their back so pushing a tile can move it and, if cracked, break it in two.
Take care and don't apply too much pressure.