Yes.

One of the landmarks in vacuum cleaner history was in 1901 when vacuum cleaners were used on the carpets and cushions of Westminster Abbey for the Coronation of Edward VII. It had never been vacuumed before, and produced three ~~~trucks~~~ tons of dirt.

The carpets had been there before the vacuum cleaner, so the answer is yes, such rooms did exist.

edit:

I found my source. Panati's Extraordinary Origins of Everyday Things, Charles Panati, 1989. The Westminster Abbey produced three tons of dirt.

I got it confused with the cleaning of the Crystal Palace which was being used to house sailors in WW1. That operation produced "26 truckloads" of dust. There is no information on the capacity of the trucks.

Yes, absolutely, there were carpeted rooms in Victorian English upper and middle class houses, as anyone who has read any literature from the period carefully will confirm. Sherlock Holmes, for instance, was always tracing footprints on the carpet, or prying loose the nailed down carpet to look for clues underneath, and he also had the annoying habit of dropping his cigarette ashes and ends on the carpet sometimes out of laziness and sometimes by cunning design:

I could see no marks to guide me, but the carpet was of a dun colour, which lends itself very well to examination. I therefore smoked a great number of those excellent cigarettes, and I dropped the ash all over the space in front of the suspected bookcase. It was a simple trick, but exceedingly effective. I then went downstairs and I ascertained, in your presence, Watson, without your perceiving the drift of my remarks, that Professor Coram’s consumption of food had increased—as one would expect when he is supplying a second person. We then ascended to the room again, when, by upsetting the cigarette-box, I obtained a very excellent view of the floor, and was able to see quite clearly, from the traces upon the cigarette ash, that the prisoner had, in our absence, come out from her retreat.

Source: Doyle, Arthur Conan. The Penguin Complete Sherlock Holmes. Penguin UK, 2009.

In the absence of vacuum cleaners, Victorian householders used that plentiful resource: servants. It was the housemaid's duty to daily sweep the carpet, after having strewn damp used tea-leaves over it:

In a quiet country house, with a garden lying round it, free from the dirt of a city, and at a season when there is no dust from the fires, carpets do not want sweeping so often as in a town, or in winter. Once, or at most twice a week is sufficient. When the sweeping is to be done, however, it ought to be thoroughly done. There are some houses where, if a visitor chances to cast an eye under the sofa or piano, the carpet looks a different colour from what it does every where else, from the quantity of dust lying upon it. The proper way is to cover the sofa with an old sheet, kept for the purpose ; to hang up another sheet before the book-cases (if they have not glass in front, to protect the books from dust), and then to sweep out every corner of the floor, shifting the sofa and tables so as to get at all the dust that has gathered under them ; and, if there be a recess or dark corner in the room, to take more care about sweeping that than any other part, instead of trusting that the mistress will not look into the corners to see how the maid does her work. The tea-leaves of the family-table are all to be kept by the housemaid for her sweeping. Strewed damp upon the floor, they collect the dust, and prevent its flying about, just to alight somewhere else.

Source: Anon (c. 1870) The Housemaid and Her Duties and How to Perform Them

This is confirmed by the excellent and renowned Isabella Beeton in that classic of Victorian household management, Mrs. Beeton's Book of Household Management (1861):

After breakfast, except her attendance on her mistress prevents it, if the rooms are carpeted, she should sweep them carefully, having previously strewed the room with moist tea-leaves, dusting every table and chair, taking care to penetrate to every corner, and moving every article of furniture that is portable.