The shops are a red herring, really. The fact is that it is a public road (or an offshoot of the main one) with available first-come-first-served parking spaces for anybody to use, for any purpose - be it parking outside their home, parking to use a shop or just parking up to have an urban in-car picnic.
Assuming there are no restrictions in using the parking, the homeowners could presumably nab a space and park there on the road outside their house for as long as they want. But I'm guessing that they also want to be able to have guaranteed parking waiting for them when they leave the space to take the car out somewhere.
They would need to apply to the council (and pay) to drop their kerb officially, if they want to use their self-created parking space on their property and have permanent clear access to it. The council don't simply physically drop the kerb, but they also verify and approve whether they deem it appropriate to have a guaranteed exclusive access for one property there, and they have to ensure that the pavement is/can be made strong enough to facilitate the weight of a vehicle regularly passing over it without risking damaging pipes or cables underneath.
I think the overwhelming likelihood is that the council would not approve this - hence they have arbitrarily decided what they reckon is 'right' (and just so happens to suit them) and are now exercising that self-granted 'right' - not unlike a cat who has decided that a neighbour's garden is its own territory to wee and poo in, and fiercely chases away any other cats who try to muscle in.
Unfortunately, they don't sound like reasonable people, so although you would have the perfect right to park on that bit of road, as you say, you can't know whether they will react by criminally damaging your car or similar.
In some cases such as this, councils have installed strong bollards (or 'conveniently' situated road signs) which physically block the homeowners from being able to unofficially drive across the pavement to park on their property.