I don't see why they closed the business rather than renting a registered address and just continuing to work from home though. If it was online sales only and they didn't have customers coming in and hadn't changed the house to a warehouse or anything like that.
How on earth is that going to work? A currently works based from home, but would not only have to factor in the considerable costs of a registered address but would also have to move to be based from there for accepting deliveries, packaging and dispatching. Effectively move there and be unable to do anything throughout the day that needs doing at home or looking after children.
Unless it is constant deliveries, there's nothing wrong with running a business from home, as long as you don't regularly have customers visiting the premises.
So many people have been working from home throughout Covid; many will be continuing to do so for the foreseeable future. I don't think it's sustainable for people to expect no crossover whatsoever between working and living in residential areas.
As for B's complaints, we don't know how much they may have embellished their story, made a scene, got other neighbours on their side, have links with/a relative on the council etc.
'Causing inconvenience' is very vague indeed - it sounds to me like the equivalent of 'driving without due care and attention', which is extremely open to interpretation for a police/traffic officer who needs a justification (whether fair or not) for fining/prosecuting you.
As PP have said, like it or not, large vehicles do visit cul-de-sacs and other small roads a lot - deliveries, residents parking works vehicles, emergency vehicles, tradesmen doing work for residents.
Always makes me think of the snobby neighbourhoods where they throw up their arms in horror at the very notion of a resident owning a commercial van in their 'decent' street, but they never complain when they need a builder/plumber/electrician - who obviously resides and parks their van somewhere else - to come to do work for them.