I'm sorry, i was impatient. I apologise. AAMOI, i've now looked at the pic more carefully, and notice what i should have seen immediately: that the ceiling is lowered.
You cannot skim over the tiles. However, you can probably fix p/b thro the tiles to whatever backing the tiles are fixed to and then skim the board.
Whatever you do, you must first do some destructive investigation, and open up the ceiling to determine how it's constructed. You must have something, and know it's location, to screw into it.
New cove or trim can be fixed later.
Soundproofing, esp retro soundproofing is a complex issue. Perhaps the 400mm cavity is the best soundproofing available to you without opening up the ceiling.