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That makes you more contractory.
Which is good, as you wouldn't be caught by IR35.
In the other circumstance, you could be taxed as an employee, under IR35 (and the employer may be taxed NI etc...)
BUT it would be tough to succeed in an employment rights claims.[Edit] I'm way out of date on this stuff...
You still seem to have an employee relationship with the first company, given the tests.
Other people do this, or you work at other companies?
If it's other people, it sounds like you are a worker, as most of the tests for self-employment / contractor would be failed.