Peggie_Py's solution also worked for me. Thank you Peggie!
Before coming to the forum, I had removed many third party apps (in case one of them was causing the issue), had switched on and off the phone many times and was about to completely "reset" the phone. Also began looking at new phone options.
To make it work, I played music on the walkman and kept inserting and removing the headphones while music was playing, kept starting and stopping the music, eventually the internal speaker began to play again without the headphones.
Phone now works OK for phone calls without using the speakerphone.
It is a shame that Sony have not released a patch for this headphone problem, given it is so widespread and causing issues for people.
I am sure many Xperia users have not known where to look on the internet for a solution and have abandoned their Sony phone and purchased an alternative brand instead. Sony needs to be proactive re this situation.
Hope this post helps other people to solve their "Sony Xperia only works on speakerphone" problems.
PS. I see other people have had success by cleaning out their headphone socket, I tried that but it made no difference and the socket was clean (no obvious fluff or dirt). Perhaps it is a combination of hardware connection issues, plus software glitches caused by the insertion and removal of the headphones.
