Limited companies must keep company money separate from their owners' money, so they need a business bank account in the company's name. A company is a separate legal entity, which means the money in it belongs to the company, not to you.
Sole traders are not legally required to have one. You and the business are the same legal person, so you can run business income and expenses through a personal account. A separate account is still strongly recommended because:
If you run a limited company, avoid paying personal costs from the company account. Anything you take out needs to be recorded as salary, a dividend, a director's loan or an expense claim, and mixing the two creates tax problems.
Legislation: Companies Act 2006, section 386 (duty to keep accounting records); Taxes Management Act 1970, section 12B (records for tax returns).
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