I recently acquired dual citizenship (South African and British). I live in the UK. I have a question about which passport to use and when.
I think its easier to use a recent example. I travelled to Turkey for holiday but to enter Turkey you need an e-visa which can be applied for online. I found out that South Africans don't have to pay anything for the Turkey tourist e-visa (but the British do and its £20). So I applied for the tourist visa with my South African passport details and booked the flight using my South African passport details.
When I left the UK I checked in at the flight desk with my SA passport and showed them my Turkey e-visa. No problem at all.
When I arrived in Turkey I went through immigration with my SA passport and e-visa. Again, no problem.
When I needed to leave Turkey (holiday was over!) I gave the check-in desk my SA passport which started some problems! Unfortunately they were all talking Turkish but finally someone said to me that there was a problem letting me on the plane as I didn't have a UK visa in my SA passport which would allow me entry to the UK (FYI: My SA passport had been renewed recently so it didn't even have the ILR stamp in it).
I then explained to them that I had a British passport as well and they all laughed and said: Why didn't you just say so! And they issued me the ticket and I went through Turkish immigration with my SA passport to get the exit stamp and all was good. When I arrived in London I used my UK passport.
Having thought about this, what is the correct way of travelling on two passports (taking the above into account)?
There will be times when I want to travel on the SA passport as tourist visas are cheaper/free (India is a good example as well as Turkey) and I will most definitely need to travel to South Africa on my SA passport.
From what I can tell, the problem is that the airlines are doing a visa/passport check before checking you in.
So using my holiday to Turkey as an example, how should I have done it?
1) Which passport should I have booked my flight with
2) Which passport should I have used to check in with when leaving the UK
3) Which passport should I have used when leaving Turkey
Can someone assist please?

I do realise that I need to enter/exit the UK with the British passport (same applies to entering/leaving SA with the South African passport) and that I also need to enter/exit any other country with just one passport (ie: don't enter on one passport and then leave on another)