One of the definitions of very (#6 at the link) is as a synonym for actual, which is how it is being used here.
This serves as an intensifier. It's not their existence as farmers, but their actual existence as living people that was dependent on food production. These farmers had to successfully produce food or die of starvation.
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.
Best Answer
You're not looking for the meaning of "be very much"; you need the meaning of "be very much for", which is an idiom.
To be for something is to be in favor of it, to be an advocate of it, to be a proponent of it.
To modify it with "very much" is what it sounds like: to be particularly strongly or enthusiastically in favor of whatever it is.
In this case, the teacher was surprisingly (to the narrator "I") in favor very strongly of the planned excursion.