Ours are semi-floating, with a wave washer snugging the fit. The washers get dirty or worn, resulting in lateral movement of the disc. This lateral movement can cause noise. It's annoying more than anything else.
That stated, full-floating discs have quite a bit of play as they aren't snugged to the hub by washers. Full-floaters are considered state-of-the-art despite their rattling, clanging, whirring, and vibrating nature. While riding down a bumpy road on full-floaters, you would swear your bike is grenading from the sound.
The semi-floating discs on US models are held to hubs by rivet; However, I believe UK models are held by circlip. If true for your bike, just remove the circlip and replace the offending washer(s).