"thank you very much" in your question means appreciation. I use the fact as an example to make the answer more clear. The fact: When I was ranking the first place on Italki top 20 members board. Some one sent a complaint to Italki, telling them that all my answers were wrong. Her intend is telling Italki that I am the phony. If there is some one who oppose, send an email to italki, telling them that my answers were not all wrong. He/she defense me that I am not a phony. In this situtation, I would say "Thank you very much" to that person. It is an appreciation. In your question " Mr. and Mrs. Dursley... were proud to say that they were perfectly normal, THANK YOU VERY MUCH". In this case, Thank you very much is an appreciation to Mr. and Mrs Dursley for their opinion of "perfectly normal".

The fact that THANK YOU VERY MUCH is written in capitals puts an emphasis on this phrase and the couple are shouting to everyone loud and clear that they are normal.The author meant it to be sarcastic because the couple did not act normally at all.

"Thank you very much," in that context, means something like: "thank you very much (for asking); glad you asked." or "Thanks (for asking), but no thanks!" like: "I can manage just fine, thank you very much!" It's a pre-emptive reply, as it were, to anticipating someone asking whether you need help or some such. It's often meant a bit sarcastic. Like when I say "I can manage just fine, thank you very much!", meaning something like: "No need to ask me, offer me help, as I can do this perfectly well by myself."

In this context, it's meant to be sarcastic or snippy. The German translation basically has the meaning correct, but without the edge. It sort of preempts the idea that someone would say differently. It's also often meant to end the line of conversation. An example would be: "Those bags look heavy. Would you like some help?" "I am perfectly capable of carrying my own bags, thank you very much." The implication is that the person saying "thank you very much" is annoyed and/or affronted by the idea that someone would think that he/she looked like he/she needed help. In the case of Mr. and Mrs. Dursley, it means that they're preempting the idea that someone might question whether or not they were normal. It fits in with the fact that they hate anything to do with fantasy, magic, imagination, creativity, etc. If you can get your hands on the audiobook version of the books read by Jim Dale, you might get a better understanding of the tone used in the books, which I often find very helpful in figuring out what things mean. Hope that helps! :)

In this context, it appears to be sarcasm (сарка́зм). They are not truly appreciative.