I feel it's better to think in terms of Annual Salary like you would do for most other jobs. It them makes it easier to compare, though as you say the number of hours worked is also a major factor. Full-Time jobs some people do are 35 hours or so. For a nanny, full time can be 50-60 hours - it's like working a job and a half or two thirds.
Your location can affect how much childcare costs. In a city, childcare costs can be higher than say 20 miles outside of that city. Without knowing a huge amount more about the job and your location, I don't feel we can say if the amount you are agreeing to pay is reasonable or not. Even with a lot of information, we probably can't really say if it's reasonable or not as what is reasonable to one person, is not reasonable to another.
Your friend isn't the one employing this nanny, you are. So does your friends view on how much salary you are prepared to offer the nanny matter at all to you?
The agency I feel should be telling you to agree a Gross salary - it's a pet hate of mine about agencies, they still seem to think nannies are not real employees like everyone else - does your own job pay net? I doubt it.
Using www.mranchovy.com/calc/ £9 net per hour, equates to £12.02 gross per hour, based on 55 hours per week, 747L taxcode, no student loan. So that's £38,266 cost to employer (once adding in Employers NI) - Note Employers NI I think goes up in April 2012, so your cost will actually be higher than this.
Remember that you are the one offering the job, so you dictate the terms of the contract. So if you want to offer an annual salary (say £34,000 gross) then you can do so. The nanny may want to know an hourly rate, which could be provided as a Gross amount. Then the nanny can use PAYE calculators to get an idea of what their take home pay would be, depending on what their taxcode is at the moment. If you agree a Net wage, then keep in mind that a taxcode can and often does change. So you could find you pay More, or you may find you pay Less. Can work in your favour sometimes but I feel all employees should be paid on the same sort of terms... why are nannies the only ones to get Net pay deals (I don't think anyone else gets pay done that way, do they?)