Cleaning question

[Filbert]

I am in the process of moving into a new flat and which had been uninhabited for at least 6 months before we came along.
The bathroom is in a bit of a state. The bath which is white has black streaks in it which refuse to come off with the Spanish version of Mr Muscle (I live in Spain). Also the white toilet has black residue at the bottom which won't shift either. Any ideas as to how I can make them look spanking new?
Thanks in advance. I warn you, more questions to follow regarding decorating and hanging tips as I am a complete novice...

[sense4all]

Can you tell us what the bath is made of eg enamelled metal, porcelain or plastic. As this really matters for cleaning remedies. ta!

[Filbert]

Do you know what, I'm not entirely sure, but I think its plastic

[winny]

Here in england we have Cillit Bang spray stuff you can put on enamel,tiles,plastic and pot. It is brill.