Am I personally liable for my business debts as a sole trader?

Yes, as a sole trader there's no legal separation between you and your business, so you are personally liable for any business debts, and in the worst case creditors could pursue personal assets. This is the main trade-off against the simplicity of the sole trader structure, and it's a key reason some people move to a limited company as their business grows or takes on more risk. Business insurance (such as professional indemnity or public liability) can help manage some of that risk even while trading as a sole trader.