I do not know if SA in Windhoek will check bags through with BA. Considering that if you were flying BA to Johannesburg and connecting onwards to London on BA but on separate tickets that BA would not check them through, I am doubting that SA will be able to check them through.

Cape Town is generally a very efficient airport, and I personally find bags generally come off very quickly. I have also checked the on-time performance for SA8127 01 July - 31 August 2018 - it shows on-time for 59 days, late 1 day and excessively late 1 day, so pretty reliable that it will arrive on time. The only concern would be that you have EK770 from Dubai scheduled at 16:30, so if it is a bit late and you get caught up in that, it could delay you a bit.

From exiting customs you have about a 150-200 metre walk to escalators that take you up to the departures area where the British Airways check-in desks are based.

Theoretically if all flights are on time you could be sitting in the lounge within 45 minutes of landing. That is in ideal conditions, but it doesn't leave you much wiggle room if things go a little wrong.