I'm self employed, have been for about 10 years. Over the last year I've been working more and more for one customer ( X) , not to the exclusion of all others, but I guess I do 2-3 days a week for customer X and only about 1 day a month for any other. Across a year I probably work for 5 or 6 customers.
I think I'm still in a self employed position, I pay my NI, I have my own PLI. The days & times I work for customer X are negotiated between us. I work sometimes at Xs premises and sometimes at locations determined by the work X needs done, occasionally I work at my premises on Xs projects. I supply my own basic tools, X supplies some more specialist tools and a vehicle to transport equipment to site IF needed.
X has been asking if we are SURE I can still be considered self employed. I think Yes, X seems to be wondering if they ought to be employing me. X has employers liability insurance and does on occasion employ people. I'm not so sure they would be willing to pay me as much as an employee as they pay for my services now.