Finding Cheap Flights- Any software?

It's my 50th birthday next year and I want to celebrate by having a holiday in New Zealand. For the last couple of months I've been trying to book the flights but I'm getting nowhere fast. I always have the same problem when looking on the internet for flights. The websites have tempting offers like "London to Auckland from £519" but then when you try to find out more it gives you a form to fill in, asking what dates you want to travel. You then enter some dates and it comes up with a figure about twice as much as you had hoped to pay. I'm wondering if you can get software that will go through every possible date to find which is the lowest fare? I'm thinking of something like the automatic bidding software some people use on Ebay to make multiple bids in the last few seconds of an auction. I suppose it's possible that these cheap flights simply don't exist and the system is designed to make it difficult to prove that they don't exist.