I had this the last time I travelled to UK (April last year). I've always kept my UK passport and became Aussie in 2002. I had not had a problem before but this time I put in my UK passport number with Qantas. I couldn't check in online and at the desk the lady said she had seen this issue before and needed to call Immigration. I looked worried but she kept reassuring me all was OK. She linked up the passports on the phone and then all was good. I couldn't scan out of Australia at the automatic gates but the staff checked both passports manually and said it should be OK the next time...
I am flying to London from Hobart via Perth in a few days - interested to see what Hobart check in do. This time I haven't entered either passport and will just handover both and say "do your thing" in the system!
As an aside, I personally don't get the whining. UK passports are cheap and easy to renew. Why pay loads of money to renounce your citizenship or pay for a certificate of entitlement when you can get a cheap passport that is valid for 10 years? I also saved a fortune in Chile, Brasil and Viet Nam where no visa needed on the UK one.