7) ITA Matrix
ITA Matrix is a Google owned platform which is a really useful tool for finding a fare. I used it probably daily. Now this is just an introduction, since there is a proper forum in Flyertalk for Travel Tools, and that forum has several active threads in it giving useful advice. It doesn't make sense to duplicate it all here. However here is a screen shot, where I have asked ITA Matrix to show me the fares in Business Class for
oneworld flights from Amsterdam and Rotterdam to Dubai on some given date ranges. You can tailor this screen in all sorts of ways, for example making it BA only, but this is just to get you started. You need to click on Advance Controls to get access to steer towards specific airlines or routes.
https://matrix.itasoftware.com/
If you are new to ITA, I would perhaps enter the above information first, see the results and then edit the query to suit your circumstances. If your dates are totally fixed then use Select Exact Dates. ITA isn't foolproof, but the more precise your query, the better chance it has of finding your best fare. For the departure line you can put in multiple start points but they must be in the same country. For the destination there is no such restriction, but if you set the query too broad it's more likely ITA will miss something.
Best search locations in Europe for Third Country Itineraries
From a BA perspective the following locations should be considered
LON, INV, JER
DUB, MXP, FCO, PMI, BCN, MRS, NCE, DUS, TXL, AMS, LUX, BRU, OSL, CPH, ARN, GOT, HEL, LIS.
A lot will depend on the local market conditions, so LIS may be useful if BA is competing on TAP's routes, such as to Brazil.