Littering and cigarette stubs

I received a Fixed Penalty Notice for stubbing out a cigarette, surely that can't be considered as littering?

Wrong, litter includes not only cigarette butts but chewing gum also.  In many ways these items are more of a nuisance and more expensive to clean up than other items of rubbish.

But cigarette stubs aren't really waste as they can't be placed in litter bins because they will catch fire?

Smokers are responsible for ensuring they completely extinguish their cigarettes before placing them in the bin.  Cigarette waste is the same as any other waste in terms of litter laws and you can be issued a Fixed Penalty Notice for not disposing of cigarette stubs properly.  Obviously care should be taken to avoid any risk of fire and in particular cigarette ends should be completely extinguished on the stubbing plate provided on many litter bins before the stub is thrown into the bin.  There is also no reason why smokers (who are well aware that their habit means they will be faced with disposing of their cigarette waste) cannot carry portable 'butt bins' with them or create their own by carrying some soil or sand in a small tin.