As Pohutu says, you might find it cheaper to book on-line from UK sites. You may find that not all UK agents will let you do it, since some insist on a UK address, or at least they used to. This may have changed however now that e-tickets are the norm, so I'll give you some pointers. No single site is
always cheapest, but one that is pretty good most of the time nowadays is
www.lastminute.com . Do a flexible date search.
Try also
www.travelsupermarket.com and the less user-friendly
www.kelkoo.co.uk , which are both price comparison sites dealing with a number of agents. Before using these, check with Royal Brunei's website to see which dates they fly the route (I don't think it's every day), and concentrate your searches on those dates. They're not
always the cheapest to fly with, and there are two stops for refuelling as well as one for a change of aircraft, but their fares are generally pretty good, and last time I went from the UK to NZ the experience was just about bearable. Take a good book and/or an ipod though, because their in-flight entertainment system is hopelessly unreliable. You'll nearly always get a better fare booking your flight through an agent than direct with the airline for reasons I don't understand. You would think the opposite would be true, wouldn't you?
I endorse Hartington's comments re. the no-frills options, and unless you fancy long (planned) stopovers en route, it would only take one late arriving flight and resultant missed connection for your cunning plan to end up costing you substantially
more than flying with a normal airline. As long as the connection time you've allowed is reasonable, it's possible that your travel insurance might cover such an eventuality, but it'll take months to recover your costs, which is not ideal if you're short of funds.