If you enjoy risks then the 0600 from Victoria is the absolute latest train you could get, and a taxi won't get there in time if that train is cancelled or missed. Personally I'd be aiming for the 0505 from Blackfriars so there's enough time to not rush breakfast in the lounge. This means that the "night in London" is not really happening unless you don't want a proper sleep.

I don't really see how travelling to a Gatwick (or even East Croydon) hotel at midnight is wasting a night; it's probably cheaper too.