You need to make sure you satisfy the self employed criteria Will you be able to set your own hours? Will you be able to substitute someone else to do the work? Will you supply your own materials? Will you work for more than 2 people?
15 hours a week at £10 per hour, you will not pay tax on that if its your only income. You will have to register as self employed with HMRC and pay NI direct via your bank account, its a small fixed amount per month. Howeever once registered as self employed, it can be hard to get benefits etc if the work finishes. If however he employs you as an employee, he will be liable for employer's national insurance, and you will have all the protection offered by law to employees, paid holidays etc. If you are only working for him, and not working for 2 or more clients as the previous poster said, then you are probably an employee anyway. As someone just now packing in working as self employed due to all the hassle involved, I'd say be an employee.
I'm self employed and employed (2 jobs) and I'd rather get paid a little less and be employed. As self employed you don't get sick pay, don't get maternity pay or holiday pay. The person you're working for can cut your hours without notice, leaving you in the poop. Employed people have far more protection against things like this.
It's very unlikely that 15 regular hours a week for someone at their offices doing admin would class as self employment, unless you were a virtual assistant with your own business and several clients. Employment status isn't something you or the employer get to choose, it is what it is.