I'd also say look at the airlines website. Increasingly these days I seem to be getting the best prices by going direct to airlines/hotels websites, and not using agents at all.
Skyscanner is often a good starting point. It's not infallible but it can suggest routes and operators, with low prices, that you might not otherwise consider. For example, there seem to be some good deals from Heathrow to Narita, with Alitalia, via Rome: http://www.skyscanner.net