Removing silicon sealant from ceramic and plastic - please help!

[MakesCakesWhenStressed]

We have a house with a new bathroom and there's a film of silicon sealant over some portions of the basin (ceramic) and bath (plastic). This obviously makes them very difficult to clan - especially since we live in a hard water area so are battling awful limescale as well!

Any ideas? Scrubbing with microfibre pads and rough sponges doesn't do anything and I don't want to scratch the ceramics/plastic

[Anthracite]

You need to buy a special solvent. It's called silicone seal remover.