I would call the room "the laundry", without specifying the word "room". In fact, the phrase "kitchen and laundry" commonly appears in advertising (particularly real estate listings).

Here's a quote from an arbitrary commercial page which showed up when I searched for "kitchen and laundry":

The laundry is the engine room of your home, helping you keep everything in perfect running order. With our extensive range of laundry tapware, troughs, wastes and more you can create a laundry space that will look great and be enjoyable to use.

That is an Australian site, and I grew up in New Zealand, but the Oxford English Dictionary provides a definition includes a definition without indicating country-specific notes:

2. A room in a house, hotel, or institution where clothes and linen can be washed and ironed: the pathology department was in the hospital basement, next to the laundry

In contrast, Merriam-Webster (an American English dictionary) does not specifically include the "room" definition - it uses the more general "business or place":

a business or place where clothes, towels, sheets, etc., are washed and dried

I would call the room "the laundry", without specifying the word "room". In fact, the phrase "kitchen and laundry" commonly appears in advertising (particularly real estate listings).

Here's a quote from an arbitrary commercial page which showed up when I searched for "kitchen and laundry":

The laundry is the engine room of your home, helping you keep everything in perfect running order. With our extensive range of laundry tapware, troughs, wastes and more you can create a laundry space that will look great and be enjoyable to use.

That is an Australian site, and I grew up in New Zealand, but the Oxford English Dictionary provides a definition includes a definition without indicating country-specific notes:

2. A room in a house, hotel, or institution where clothes and linen can be washed and ironed: the pathology department was in the hospital basement, next to the laundry

In contrast, Merriam-Webster (an American English dictionary) does not specifically include the "room" definition - it uses the more general "business or place":

a business or place where clothes, towels, sheets, etc., are washed and dried

The comments on this answer (and, indeed, other answers) suggest that American English does not use bare "laundry" to refer to a room in a house.