Is lip grafting still available, and will it help reduce the length of the philtrum?

I dislike my long philtrum but I have a lot of tooth show so I don't think I would be recommended for a lip lift. I'm wondering if lip filler would reduce the appearance of my long philtrum instead. If I liked the fillers, I would want to choose a more permanent option such as lip grafting, but I can't find any information online about this procedure so I'm not sure if the procedure is still available in the UK.