As soon as you work through an Umbrella Company you must set aside any idea that you are “Self Employed”. You become an employee of the Umbrella Company and it is in that capacity that you would be working. The Umbrella Company is your employer.
All UK employers, including umbrella companies, are required to make payments each month to Her Majesty’s Revenue and Customs (HMRC) for Employers’ National Insurance Contributions. Whilst you may not be liable to pay Employee’s NI contributions your employer still has to pay Employer’s Ni contributions and would make that payment to HMRC from sums received in respect of your assignment work.
Unless the relationship is direct with an end client it would not be for the Umbrella Company to negotiate hourly/daily rates of pay. That would normally be done by the recruitment agency.