Send reminder before Late Payment request?

I have 2 question I would like help with please. I used to get work off a firm many years ago but I stopped working for them as they were always late paying my invoices; I am a sole trader. Perhaps I should have learnt my lesson but out of the blue they sent me another job in October 2012, which I completed and invoiced on 9 October 12 for £75, terms were 30 days. I view of their history, do I need to send them a reminder letter requesting payment first, or can I just send them the late payment charge? I realise it might be bad business practice but I wont be working for them again & I just feel like 'going in for the kill'!
My second question is how do I actually apply the late payment charge? After looking on this great site I think I just send a separate invoice showing the 'original' amount owed (£75.00) and then I show/add the late payment charge, making the new invoice total now about £116. Or, do I just send them a copy of the original invoice together with a new invoice just for the late payment charge? Thanks for any help.