then on that basis any landlord is exposed where a tenant carries on a business without its consent.
I think so... yes.
Edit: Just read mrsdawrazer after my own post. My parents had this happen with a chap wanting to fill gas cylinders under a timber house. Thankfully he asked for their permission, which they refused. Had he not asked, my parents would still have been liable (my understanding of it).
My parents suggested he hire a commercial place to do his business, and he did move. He could easily have moved to another residential house and simply decided not to ask permission of the next landlord. Scary indeed!
They also had a lady bringing children into an IP to teach music. She had no public liability policy of her own, and moved rather than buy one. That also was a risk to my parents.
We have rented to people who have run business from home, and insist on sighting their public liability insurance. After sighting the policy and taking a copy, we have no idea if they cancel it, and yes... it is a risk for us.
I was told several years ago that one tenant who ran a business from home was okay without a separate policy as he had nobody call to the house to conduct business. I believe it is when a business has customers calling to the house that it becomes problematic and they need a public liability policy.
I believe there are thousands of landlords who have no idea of the risk they are at if a business is being run without their knowledge (depending on the business and a few other things as above).