Whilst you dont need public liability unless people are visiting your place of work, it might be worth considering what happens if you go to a clients home/office and damage something (ie; spill a cup of coffee on an expensive rug/carpet)? Public liability would cover the cost of repair or replacement in that instance.
You also need to consider professional indemnity insurance. If you inadvertently break copyright law or if a client decided that your work has damaged their business and takes you to court, as a sole trader you could potentially lose everything including your home.