even though people like Peter Chester are in jobs which pay high salaries.
Pre NHS, country/small town GPs like Peter Chester probably didn't make a huge amount of money. Most of his patients wouldn't be very well off and wouldn't call the doctor very often, and Peter probably kept his fees low and didn't press for payment. If he did his own dispensing he might've given away medicines too rather than charging for them.
There were sickness clubs, as Alison says. But unless you could be absolutely certain of keeping up the payments, week in, week out, there was no point.
If you missed a week, say because the husband had been laid off work, membership lapsed and you lost everything you'd already paid in. For many people it came quite low down the list of priorities, after rent, food, fuel, etc.
I think EBD was middle class by virtue of her profession(s), but her origins were lower
middle class. She could write very convincingly about things she knew about - teaching, music, etc. - but she didn't really know first hand about landed gentry, world-renowned specialists, and so on.
Similar is said about Dorothy L. Sayers, country vicar's daughter, writing about the aristocracy. Harriet Vane is much more realistic, because DLS knew about Oxford and writing.
(Come to think of it, Harriet's father was a country doctor who just managed to put her through Oxford, but didn't have anything to leave. Harriet says that since leaving Oxford everything she's had, she's earned herself.)