There is a lot of tabloid trash published about the Royal Family, it doesn’t make it true but unfortunately a lot of the trash continues to be peddled with the justification “Oh I read it somewhere”.
The off the shelf quick result pregnancy tests we have today, simply did not exist in 1952, so Queen Elizabeth could not have been tested in the swift conclusive way you suggested. She would have had to undergo a detailed medical examination and even then doctors may not have been able to conclusively confirm yes or no dependant on how far advanced the supposed pregnancy was. While she likely had her own doctor at Sandringham, it seems unlikely he would have been considered appropriate to undertake a thorough gynaecological examination when the issue at stake was the throne. So who did it?
There was no delay in the proclaiming Elizabeth II as Queen because of the prospect of her mother being pregnant, although there seems to have been some delay in notifying her. She was in a different continent and there does seem to have been some issue in contacting her as she was in the wilderness in Kenya.
No serious biography of either Queen Elizabeth II or her late mother Queen Elizabeth, I have ever read has ever suggested that the prospect of the widowed Queen being pregnant at the time of her husband’s death was ever explored and the death of the King and succession of the Queen has been written about extensively.
Rather than just acknowledge its nonsense or reference the book you claim said it, it is completely absurd to try and justify your original comment by a reference to the Spanish situation, which is quite different in circumstances where Queen Maria Cristina and the Spanish prime minister knew she was pregnant at the time of her husband’s death.