German phonetics

Does anyone have experience of being taught German phonetics? And can you recommend a teacher?

I thought my accent was okay-ish until I heard Prince Charles talking at the Reichstag and apparently my German is as heavily accented

Unless you are working as a news reader I would not put too much worry on it as practice makes perfect, as they say.

Is it just to blend in or is it actually hard to understand what you're saying?

Based on my experience with learning French as the listening skills improved, the clarity of my speech also improved, even though I didn't do any phonetics training as I found it irritating. Just do conscious listening to a good quality model pronunciation every day and your brain will pick it up over time, such as selected TV or radio shows/news