Ways to get into sound/audio engineering

Hi, I'm 25 and I live in London, UK.

I'm looking to get into sound engineering. I've not got a music/sound engineering related degree, having studied economics at Uni. However, I have a strong musical background in classical music (play piano and oboe).

I'm interested in music production in my spare time - using Ableton - and have a general understanding of production and music theory. I want to know what is/are the best (and ideally value for money) routes into sound engineering. Are courses a must to get any related job in sound engineering or can a portfolio of production work lead to being taken on in some related role and learn on the job?

Also, any insights into the sound/audio world would be helpful as whilst I have an interest in the technicalities of sound and a decent ear, I want to know what some sound engineers love/hate about their job?

Thanks a lot!