The Lakeland things are very good, but fiddly and will make you swear quite a lot. I have some cotton gloves that wet with solution of warm water and Pledge wood soap and go along the slats of my wooden blinds.
Nancybotwin has the right idea though - if you keep on top of the dust with the hoover attachment, it does help.

Throw them away. Get curtains!

I was going to say put in bath and shower them

I've got wooden ones and just clip them off and hose them down in the shower - they dry off really quickly.

But what if they are wooden ones? Surely hosing down is only appropriate for metal/plastic ones?

take them down, lay them flat in the garden on a sheet and wash them with a sponge and hose them off. Leave to dry over washing line and re-hang. use damp cloth to wipe up any drips. (Can do this in the bath if no garden area).

Sounds like a performance but it is nowhere near as fiddly as wiping each slat!!

(I have 8 long thin ones in my kitchen/diner!)

It's got very bad reviews on their own website though...

I do use a hoover attachment on mine to give them a quick clean - but it doesn't take off all the dust. The only way of getting them properly clean ime to do it slat by slat by hand...

get one of these

It's something to do with a vinegary sponge on a stick. Beyond that - who knows??