From 'bidirectional' above :
  It should be noted that the 'staying out of politics' is
  a public phenomenon. In her weekly meeting with the Prime
  Minister, The Queen makes her political stance well known
  (that is the entire point of the meeting).[1]

  While you say:
  They haven’t had a say in British policy for around 2 centuries.
  Although the monarch meets the Prime Minister every week, they
  cannot tell the PM what to do, unless it affects the royal
  family personally. The PM listens to what they have to say but
  charts their own course.

Well, it cannot be both - for all intents and purposes. Either the Queen has a sizeable influence on the general political direction of the country or she does not.

One would think her influence particularly would have gone unquestioned to a larger degree, by the PM or politicians & their constituencies in general, in that era - when the royal family enjoyed far greater popularity than it does now.

So the OP isn't too far off the mark to assume they deserve ample blame.

[1] https://news.ycombinator.com/item?id=26749513