Do tenants need to have their own contents insurance?
As a tenants its your responsible for insuring your own possessions and you are well advised to do so.
Many letting agents and landlords make a point of requesting site of suitable contents insurance before taking up the tenancy. If you are renting through an agent ask them for details of any tenants contents insurance products they can offer you. They are usually much cheaper than you expect and offer great value and peace of mind.
It is illegal for a letting agent to advise on or sell such insurance products unless they are authorised by the Financial Services Authority (FSA), or, directly regulated by a broker registered with the FSA.
You don't need buildings insurance, only contents insurance. As the tenant you do not own the building and therefore don't and cannot insure it.