They may not want relevant authorities to know that they are running a business from a residential area. (Which isn't the same as saying that relevant authorities would actually care.)

Is that actually illegal, or do you just have to register yourself and pay extra tax or something?

Another house three doors down from the removal company is running some other sort of business, which I could tell because it does have a sign up. So unless they're just tax-dodging, it doesn't seem to me that there's a fundamental problem.

Sometimes "don't run a business" is written into the rules that apply to the house, presumably as a condition of planning permission to build it in the first place; the idea being to "maintain the residential character of the area", i.e. not have lorries up and down the road all the time. That's the kind of thing I was thinking of. There might be other reasons, or there might not.

IIRC you have to actually get planning permission to change the use of the house from residential to business. The council website has further information, but I can't be bothered to go and find the relevant pages -- sorry, am lazy! But I had to look all this up when we were trying to ascertain whether we'd get hit by those sorts of laws when trying to change two flats-for-rent into one house-for-owning. (We didn't.)