I've had the idea that someone should write an "AI-based" accent trainer. The idea is to train a ML classifier to recognize some target accent, and then use that to provide the user with rapid feedback on how close they are to that accent. Ah, it looks like someone did it already: https://www.elsanow.io/
I downloaded the app and they seem to have invested well into AI.
The UI seems to be very wasteful of user time and in dire need of a UX person who cares about optimizing the process.
Fortunately, getting the AI-stuff right is enough for it to be an useful intervention.
FWIW, I just downloaded this app and tried out their diagnostic test. It gave me a rating of 94% and (correctly) classified me as a native speaker. So that's some evidence that at least the test does not have a high false negative rate.
I suggest a fast and cheap procedure:
1. Identify a person who you want to sound more like (an English-speaking actor, for example).
2. Listen to them say a phrase.
3. Record yourself while you mimic the way they say the phrase.
4. Check the recording and then return to 3 until you are satisfied.
5. Return to 2.
You don't even really need a recording; you should be able to tell just by listening to yourself speak. A recording will help you understand how other people hear you speak though, and is more precise. I expect you would see significant progress in only a few hours.
I'm not sure how much speech lessons are, but there are people who will help you learn new accents by leading you through guided exercises to help you change the way you produce the phonemes in the target language. I can think of at least a couple people I know who did this and then ended up sounding much more "native" than they originally did, where it was very clear they were second-language speakers and had distinct accents tied to their first language.
A cheap alternative might be using YouTube and material you can find online. You can lead yourself through these kinds of exercises for free; you just don't get the benefit of quick feedback from someone who can hear how well you are progressing and give specific suggestions for things you might try to advance faster.
A wild suggestion: Try voice-acting a variety of characters from TV or books.
As a non-Japanese-native, one thing which helps me shed my "foreigner's accent" is by rehearsing 'Kamehameha' and similar punch lines from Dragon Ball as a kid. Pick some of your best characters in one of their best moments and try your best to sound like them. It helps over time.
If you're willing to invest the equivalent of a few hundred Euro of your time, the Ward Audiobook Project and many others are always looking for volunteer narrators.
improve my English pronounciation
Nitpick that I wouldn't necessarily normally point out, but which seems in keeping with the topic of the post...
It's "pronunciation", with a "nun" rather than a "noun" in it. (And it's pronounced with an "uh" rather than an "ow".)
See: https://english.stackexchange.com/questions/5732/why-is-the-spelling-of-pronounce-and-pronunciation-different
There are linguistic and pronunciation resources available for actors trying to play certain voices. I am the kind of person who prefers to go structural and then let my brain work out the details of the relevant parts of the structure
Upboat for recommendation that I think wouldn't work for me but looks like it would work for many other people. It's always interesting to see those (at least for me ;) ).
If the answer is getting speech lessons, where does one buy them? Is there an online service that provides such lessons for a good price over Skype?
I guess this depends a lot on what kind of person you are. What worked for me was:
Basically exposing myself to spoken English in ways that were rewarding on their own.
I don't speak s much English as I read and write it, but speak it a lot and have no problem being understood.
It seems I misunderstood the level of English pronaunciaction you're at and the level you're aiming for. Could you clarify?
What I wrote in my comment is what made me comfortable with speaking in English. I got some compliments for my English later and some surprised answers when I said I wasn't a native speaker (which I count as weak and strongish evidence respectively for being good at spoken English). Im not sure I did much else but I might be able to write how I leveled up if I know for which level up you're looking (in case you read but don't reply: most likely the answer is practice(prefferably in a way that rewards you of it self)).
The feedback I got was that it makes it unpleasant to listen to me when I speak in English for some people.
I'm a native German speaker and learned a good portion of my English not in school but by reading English content.
As part of a New Years event we did a Doom Circle and one essential feedback I got was that I have to improve my English accent.
When it comes to my budget I'm willing to invest a few hundred Euro but not thousands.
What would you recommend to me to improve my English pronounciation?