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Toothpaste is a mild abrasive, just like car polish...
However, just like polish, you can't just slap a thick load on and leave it there lol.
Anyway that's all redundant, 1500 grit wet & dry produces great results on bad headlights relatively fast, relatively easily and for about 50p. Follow it up with some sort of polish and sealant (ask in Car Detailing) and you've got yourself a massive improvement for hardly any money and an hour or two of your time.