To reinvent the wheel ?

Yes, 'reinventing the wheel' was the first phrase that came to my mind, too. It's certainly in the same area of meaning as 'discovering hot water', but we actually use it to mean something else. If I've understood correctly, in the case of 'discovering hot water', the person actually believes that they have made some kind of momentous discovery. We use the wheel idiom when we KNOW that a particular task is a waste of time. It's often used to indicate frustration : for example, when a company has no standard procedures in place to handle a particular eventuality, and staff have to deal with it 'from scratch' every time the same problems arises. However, if you phrased it slightly differently, for example '.... and then I realised that I'd simply reinvented the wheel!' it would be understood. By the way, we are not the first forum to have discussed this. See: http://www.proz.com/kudoz/italian_to_english/general_conversation_greetings_letters/2376355-scoprire_lacqua_calda.html

I'm not 100% sure, but "Not having invented the wheel" sounds close.

I think the most common English phrase is "to see the light".