I would suggest the use of ITA matrix as the search engine will search multiple departure points across the whole of Europe in one entry. It will then provide the cheapest option either by route on ba or by any carrier. It is probably the best flight search tool out there and would be superb if it then allowed you to book. It my experience once you have fare details and structure a call to BA or other agent can produce results.
First ex Europe is not as competitive as club. I don’t know why as first is my cabin of choice (was till they increased so much in last 18 months) club on the other hand is highly competitive but as others have said not on the NSA where prices are fixed by qf / BA quite legally under the agreement. I have however fount fares ex Europe of less than £1800 in business on ek mh and ey with the best being ex ath and ist. Try the carriers websites for details. Tk also offer super deal via hog with qf ex/to hkg.
For other destinations try aa.com first if ITA matrix is too complicated. Aa.com will provide one world options as well as lowest fare and fare structure. This can yield surprising results. And price led premium options.
If you can be flexible savings can be huge. For example lhr to dps in business was recently quoted on BA.com at £21k for 4. Cx undercut to £14k but ex eu was under £10k on same BA flights. Cgk however was under £7.5 but via hkg, a route BA Newcastle said was not possible and who suggested suggested sin as it is faster, but also over £20k. I have also seen fares to bki,mnl and tpe all much less than simply hkg.
In short eu fares are substantially lower than ex lhr even in sale. A good agent or mastering ITA matrix can be very beneficial, no matter your departure point or prefered carrier.