1. Because you can get a train or drive from those locations to LHR and go non-stop. They are also the dominant carrier in the UK market generally - lots of people will go BA by default. As a comparison, BA will sell you WAW - LHR - SIN - LHR - AMS for £483.
2. Because BA's lowest fares are only available with a Saturday-night stopover, which you don't have.
3. BA's flight and hotel options are more attractive to leisure travellers - but there's no reason you can't use them for work. Flight and hotel ex-NCL starts at £1,112.
4. If you want to keep it OneWorld, QR ex-EDI is £602, or NCL-LHR-DXB-SIN on Emirates with Qantas flight numbers (so tier-point and mileage earning) is £584.