Registering as a sole trader with HMRC means that you are declaring yourself as self-employed and that you will be running your own business to generate an income for yourself. This will mean that you will assume all the legal and financial liabilities of your business yourself. Should anything go wrong with your business, you could be putting your own personal money and belongings at risk.
Forming a company will set up your business as a separate legal entity in its own right. This means that you can separate yourself from your business and protect your assets through limited liability. Should your business take off and you wish to expand further down the line, you will be in a position to accept other people as joint owners through allocated company shares.