Amber, you don't know the laws here in Australia, and I wouldn't be surprised if the same, if not similar copyright laws existed in Britain.
I don't know where you got the idea that a business is public property. It's not owned by government; it's owned by the owner of the business. Hence why businesses generally don't let you walk in off the street after hours - unlike if you felt like taking a midnight stroll through a park or alleyway.
If you are filming from the street which is owned by the government and thusly is classified public property, then you do not need to have anyone sign any release forms.
But, if you plan to film inside their premises, not only do you need signed permission from the owner, you also need permission from the occupier of the property. This is inherent in businesses owned by (for example) Joe Blogs but managed by (for example) Mr Pink.
As you will be showing it to people, you need to have them sign a location release form.
Failure to acquire the right permission can result in the owner/occupier of a business to file for trespass and copyright infringement. You do not want to be in that position.
I notice you're a sydneysider just like myself, Green McBean. You need to contact the NSW FTO for more information and clarification.