I’m pretty sure the agency’s margin is well above £3hr, judging from what employers used to pay to agencies.
I looked at some umbrella co faqs, and it seems the main thing is that, if you work for an employer, it has to pay this NI to HMRC, whereas with an umbrella, the employee has to pay it, which is about £50week. That is on top of the normal tax and NI contributions.
There are other deductions, like pension, margin, etc which add up to less than £20week, but that doesnt worry me, as its mostly the way they take their fee,
So it seems that there is a wage percentage increase (maybe 13.5%), which the umbrella co has to offer to make it worthwhile