Hi Paul,
There is a quick way and long way to find this out. Your T’s & C’s will probably have it listed (long way) or the quick way is to give the insurance company a call. Insurance companies make their money but ‘leaving stuff out’.
Public Indemnity as you know is to cover things like slipping on the floor in your premises, but outside signage is technically outside of your office.
So I wouldn’t make any assumption around it, and give them a call.
The other item to look at is that you’re set-up as a limited company, if not and an claim is brought against your business you are personally liable. Meaning they can come after all your personal wealth, home etc. With a limited company you get limited liability, as in the company gets sued not you. If they company has no means to pay it stops there.
Hope that helps.
Pete