Thank you very much is sarcastic when used like this.
The narrator is addressing the reader and actually means: the Dursley's were not normal at all. Anyone who has read the book or seen the movie knows that. The Dursley's never actually said they themselves were perfectly normal. It is a narrative device to describe how much they are really not normal or nice. It is also a use of irony.
The narrator shows they are not very nice people at all "Thank you very much" underlines that. They are very mean to Harry.
In English, this is used in speech, when talking to someone. And usually, it is used to say the opposite to a listener.
[It is not just British English.]
Person 1: Oh, they were a very warm family. Always bringing nice pastries to the neighbors and things like that.
Person 2: Is that right? All I saw was the rubbish they threw in the woods behind our houses, thank you very much.
Person 2 is disagreeing with Person 1 and using a sarcastic "thank you very much" to do so.