Absolutely. This has very little to do with the Police.
Any venue has every right to ban you if they have cause. So the question is not whether or not the Police think you should be banned, but whether or not the management of the venue thinks you should be banned.
Even if you claim that you were not involved with the fire, if the venue management believes that you were involved, then they have a right to ban you and it's unlikely that you will get the ban overturned.
In short, a public venue in this case is "private premises" and the owner and/or management has every right to decide for themselves who they do and/or do not allow on those premises.