Some landlords operate their rental business within a limited company -  so, they own the company, and the company owns their properties. But why would a person operate in this way, and what are the benefits of doing so?

Why would a landlord use a property company in the first place?
For landlords expecting property profits - or income from another source - to take them into the Higher Rate (40%) income tax bracket (for tax year 2013: >£42,475 income), using a property company enables profits to be taxed at the lower corporation rate of 20% - this is the primary reason to use a property investment company.

Landlords who use a property investment company tend to have either very high rental yields or very low gearing, meaning significant rental profits. Typically, rental profits would need to exceed £100,000 per annum for a property investment company to become worthwhile.