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The short answer is no you cannot set up a limited company and work 20 hours a week. As a Tier 2 sponsored worker, you would have to be employed by an organisation who has issued a Certificate of Sponsorship.
Your partner is able to employ you, however, heir permission must allow them to set up a company and become a director.
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If you have any further questions, please do not hesitate to ask.
Sorry for the delayed response. I have been busy with work commitments.
You are not able to set up a limited company and become a director if you are on a Tier 2 Visa.