The external area should be covered by the landlord as they should have buildings insurance. It's not the tenants responsibility to have buildings insurance as you could easily not do it and the building gets burnt down the landlord will lose out big time. Plus most mortgage companies would insist on buildings insurance which the landlord will have to send a copy of yearly to them.
Then again if the landlord is a del boy then the small print in your lease might say you are liable for external repairs. If your lease was done via solicitors surely they would have picked up on this if it was in there.