Form 10 downloaded free from Companies House. Buy some Memorandum and Articles of Association from Staples for about a tenner. Make sure they fit and you understand them.
Form 12, again from Companies House. Get a solicitor or JP to countersign this form (take a tenner cash as they just go down the pub with it - it wil take them thirty seconds)
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Shove it all in an envelope with a cheque for �20 payable to Companies House.
WARNING: Starting a company is easy, running it properly and legally is different. You are NOT a Sole Trader if you have a Ltd Company. You become an employee of the company. Better to have the company and keep it dormant to protect the name and then stay as a Sole Trader.
You do not need to register any name for a Sole Trader - don't pay the rip off merchants that want to chrge you for it