My "laundry room" is an unfinished utility room, so we don't really try too hard to keep it looking pretty. I keep a box of powder detergent, a bottle of liquid detergent, a bottle of softener, and a box of dryer sheets all on top of the dryer (we have no good place to put shelves). I have a plastic tote box full of other cleaning products and seldom-used laundry products that I keep next to the dryer.

I highly suggest some of these little holder things for central vacuum extension wants https://builtinvacuum.com/scaledgraphics/407w_50.jpg
We have the hose hanger, a little mesh bag with smaller attachments in it, and two extension wands. One wand has the power nozzle for carpets and the other wand has the hard floor tool on it, it's easier than switching attachments all the time. We used to use our central vacuum a ton but we got a Rainbow and now I use that for the weekly "deep clean" since you can add essential oils to the water and make the whole house smell nice.

Across from the washer and dryer we have a furnace and a little 4'x3' nook area on the right side of the furnace where we have the central vacuum hose hanger and attachments, a regular upright vacuum (Aerus upright), a shampooer (Aerus Floor Pro), a couple of buckets, a long duster, and a microfiber mop (Rubbermaid Commercial, we got it from Home Depot and it is a great mop. The microfiber pads are held on by velcro and it's super maneuverable). We don't sweep, we just vacuum the hard floors that we have so because we don't have a bunch of different brooms and mops, the mop just leans against the wall rather than having a hanger. In the past I've used things like this when we had a number of different brooms and mops https://www.terapeak.com/worth/wall-mounted-mop-organizer-holder-brush-broom-hanger-storage-rack-tool-tr9371/252068631326/ . We have another smaller plastic tote with regular cleaning supplies in it, and a small laundry basket where I keep microfiber cloths.

We have a clothes drying rack directly across from the washer/dryer right in front of the furnace.

To the left of the furnace we have a larger area in the corner where we store things like wrapping paper, furnace filters, water filters, a canister style steam cleaner that I've probably used three times in over a year of having, boxes that small appliances came in, and a few things that are on our to-do list to get done like new light fixtures and door knobs.

My basement is my laundry/mud/utility room with an entrance both from upstairs and the basement garage. It's "semi-finished" - no finished ceiling - too many pipes/ducts and too low. There is carpet on the floor and the walls were covered with dry wall (painted)for warmth. But it ain't pretty! It's also a catch-all and that is not going to change until I'm dead and my children clean it out. I've done multiple major clean-outs over the 33 years we've lived here, but I think the stuff reproduces. The furnace/ hot water heater and my late husband's tool bench and tools, plus a 4' tall safe are in a separate room but no door on the doorway (too low). I have tons of shelving and a large chest and a huge melamine big box store cabinet (for all my fabric scraps), plus a large closet for fabric/wallpaper/trim samples and a place for bolts of fabric. But it's a mess. It's the only place in my entire house that is not tidy, including closets. It all has to go somewhere and the basement seems a good place. It bothered my mother, and it bothers my daughter. Not my problem.

Anglophilia. I can't even imagine your stunning home being attached to an untidy basement LOL...but isn't this what unfinished basements are good for...storage.

Exactly! I don't trust people with pristine, Spartan basements or garages. We just can't be friends if they are...

In our current home, there is a hanging rod to the right of the washer/dryer. I assume it was intended for clothes being hung as they were removed from the dryer.

However, we bought S-hooks and hang our broom, floor steamer, hard floor mop, mop from the hooks and it works great. They never fall down (not something I can say about any solution we've used previously) and they are off the floor.

If that doesn't work for you, I'd recommend making sure all of the cleaning items have holes at the end of the handle so they can be hung from those--they tend to be less fragile than most of the other ways of hanging brooms/mops.

My washer and dryer of course. The hot water heater is in a closet beside the w/d and I have shelves full of detergents and odds and ends above the w/d. The cat's litter box is on the far end and there is a shelf with more detergent. On the wall is the dusters and the mop/broom/dustpan, and the ironing board with iron.

When I write that, it does sound like a lot of stuff is packed into a room that is about 5x8.

Since our laundry room is the walkway to our garage and therefore our large trash can, I keep our litter box under the laundry sink. I also keep the bucket of clean litter straight across from the litter box. I love it because the litter only has to barely come in to the house and then can go right back out. No lugging buckets of litter to basement or carrying bags of waste through the house.

My laundry room is only that; it's not a mud room or utility room. I have lots of shelves - hub built most of them and installed them. There are huge hooks he installed for me to hang clothes on (I hang and fold clothes as I'm taking them out of the dryer). He also installed a nice rod/shelf above the dryer so that I can hang or lay things there to air dry.

Other than machines, hooks on the wall, and shelves, I have lots of laundry detergent, a jug of vinegar, a huge jug of fabric softener (one lasts more than a year), a box of OxiClean and Color Catchers for when I combine colors in a load (I don't do that often, but I have a thing about only washing full loads). And a tall kitchen size trash can which seems to stay full - I haven't figured that out yet.

Mine is very utilitarian, but it works for me and is in a very handy location.

Laundry in basement, dehumidifier is necessary... :)

My laundry area is right by the back door to the garage so I have a small, soft side cooler in there I can grab on the way out the door if I know I'll need to keep something cool while I'm running errands. Also vases, and a small tool box.

I also keep the dryer vent brush/rods that connect to a cordless drill.

My utility room is separate from my laundry room. It is about 10' X11'. It has the plumbing, water pump etc. type of mechanics needed to run the house. I store all my cleaning products, vacuums, rug shampooer, soda, bottled water, vases, canning jars and extra paper products in there. It has cabinets and shelves for that but I have to keep after it as it can become untidy. It is too easy to just toss things in there and walk away.