If you start a business on your own, or with someone else, without forming a company, you will be trading as a sole trader or in partnership whether you intended this or not. You are legally required to notify HM Revenue and Customs when you do this and are likely to face a fine for failing to do so.
As you have not formed a company, you will be personally liable for any business debts.
If you are in business with someone else and are legally seen to have formed a partnership - even if you had no intention of doing so - you could be liable for your partners' business debts. You also miss the opportunity to draw up a partnership agreement to suit your wishes (see 13 and 14).