I am not 100% certain on the entry rules but from what I have heard, as she has a long-term UK visa and is living in the UK she would be allowed to enter if she made it to Germany, especially when travelling together with you. The important thing is to not be denied boarding by the airline, and the airline will use the TIMATIC rules which as far as I can see will permit entry.

If London is added after you arrive that's fine. As your flight is in the morning hopefully you would avoid the awkward situation of half the passengers needing to quarantine and half not, if it gets added while you are waiting at passport control....

The issue with testing on arrival is, what happens if you test positive? If London is added I would just take the future travel voucher from BA and wait to see what happens over winter.