Do I have to arrange parking through my local council / concierge / local authority, to obtain permits if necessary?
Yes, it is the customer’s responsibility to make sure that they have permit(s) for all the addresses concerned. No Removal Company or Removal Firm in the industry would usually take any responsibility for this. If you could not get one on time, you might be able to ask neighbours for visitors permit to use for that particular day if available and applicable.
Let your neighbours know that a removal van will be parked outside your house and may cause them inconvenience.