You have lots of options!
However, it does take a bit of work to find them. The BA site does show some availability for your dates, but only using the ARN-LCY flights which is very early in the morning (outbound) and involves a change of airport (LCY-LHR). Ba.com will only show partner flights if BA has no availability at all.
A more useful site is qantas.com (though you need to create a user profile, which is free). Currently showing many options for your preferred dates in Economy including via Berlin, Helsinki and LCY/LHR. Fewer options in Business, but more options in Business if you change dates to Sep 19-24.
Happy Travels.