Yep, I don't think they've understood/you've not given them accurate details..
You can check online, on the gov.uk site, simple online form.
The company I have a contract with do an annual test to ensure we (my direct colleagues and I) are self employed.
We set our own rate of pay - it's negotiable but we suggest what we want to be paid, they'll come back and say yes or no and we can haggle.
I can swap shifts/give my shifts to one of several other people if I want to, thats entirely between 9 of us.
We decide between us what hours we will work.
I work from wherever I want, and as long as the job is done, what else I do in that time is up to me - so if work is quiet (I have to respond within a certain time, and I have to provide a quality and useful response) I can do other work around it, at the same time.
So there are days where I am being paid X an hour from company A and I am also earning Y an hour from a private client (the client is not charged for any time I spend working for A!).
So in practice I may do an 8 hour shift for A, but only 5 hours of that actually responding to clients, and 3 hours doing some writing or illustration for B. It's not often and I don't generally like juggling both that way but sometimes I do.
I can and do also work for other people when not working for A.
I could not do any of this if I were someones employee!