I don't think so, at least not unless you're having clients round to your premises. I tend to meet clients either at their offices or at a local coffee shop. It's worth making sure any pricey equipment you need to run your business is covered in your contents insurance though, just in case.
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.