There are a number of ways at "guessing" the age of a book by style of printing, the use of colour and the style of the way the pictures are presented, to items mentioned in the text. As you have mentioned that there are pictures of early vacuum cleaners and that at least is a starting point to go from, seeing that in the first edition of Mrs Beeton's book (originally entitled, "The book of household management comprising information for the mistress, housekeeper, cook, kitchenmaid, butler, footman, coachman, valet, upper and under house-maids, lady's-maid, maid of all work, laundry-maid, nurse and nurse-maid, monthly wet & sick nurse, etc, etc, also a sanitary, medical, & legal memoranda: with the history of the orgin, properties, and uses of all those things connected with home life and comfort.") which was published in the October of 1861, has the small section (well small paragraph really) on sweeping the parlour carpet by a brush made from cocoanut fibre. This method would have prevailled until the horse drawn carpet cleaner made an appearence in 1901 when Hubert Booth drew a patent out on his devise. From 1908/09 Mrs Beeton's "Book of Household Management" (same book but the title shortened) may have been suggesting the use of the new invention of a portable electric vacuum cleaner which had been invented by the American James Murray Spangler in 1907. Spangler, having taken out his patent on his invention in 1907, sold his vacuum cleaners via his company "The Electric Suction Sweeper Company". One of his first customers was a cousin of his and her husband William, liked the invention so much that he first invested money in the company that Spangler had started and eventually he purchased the 1907 patent and became the head of the company. In 1922 William changed the company name and using his own surname it became "The Hoover Company" (just think you could be saying that you will "just run the Spangler over the carpet"..............nah just doesn't have that ring to it some how).
Getting back to the date of your Mrs Beeton's, if the pictures show an early Hoover then it could be after 1919 as this was the year that the Hoover Company opened its first factory in the UK.
old rowley