At last I've done it!
I used uk-plc.net (proof that the first option on google for searches gets the business) to register it. I'm the sole shareholder, and I'm a director and the secretory. Another family member who is already a director of another company is another director.
Now I can impress people visiting my website by putting 'Incka Limited' instead of 'The Incka Group' and I can claim computer costs against tax...
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