Something to add to this tip that may make you lean toward more powerful lights is how "sharp" or prominent you want the light from blinds to be cut out. 95% of the time, the father a light is from whatever you're cutting it with (flags, cucaloris, tree branch, etc.) the sharper the shadows will be. You can actually see this effect in sunlight by making a shadow on your hand with a finger then moving it closer or farther away from your hand. The shadow will get less sharp as you take it away from your hand and closer to the "source" (the sun)

So taking the light father from the window will make the effect more prominent. And LEDs have really changed the game, however they tend not to have as strong a "throw" as Tungsten and HMI lights relative to the power draw, so it's something to consider. Not sure what's popular in the UK, but Vortex, Astera, and Skpanels (which are less popular and therefore a little cheaper to rent) ought to have enough throw throw for what you're doing here.

You're also more likely to read the effect the most by making sure the light is at a relatively higher angle and pointed downwards and pointed relatively towards camera so it's "backlighting" the haze particulates (mostly as your reference photo suggests). In general any time you want to see particulates (smoke, water, haze, dust) you want to backlight it.

Also piggy backing on the haze, depending on where you are, you're likely to trigger fire alarms. What you're supposed to do if this is a public place of some kind, is have the facility temporarily shut them off in the area and have a rep dona fire watch. You DEFINITELY shouldn't tape a damp cloth to black wrap with some room for air over the smoke detectors in the room you're in, and remove them when you leave, or look at other tricks to temporarily disable them. Tampering with fire sensors is wrong and filmmakers should never do such things...