younger/less exp nanny for say £10/11gross... surely you mean less than that. As an older, more experienced nanny that's my sort of salary 
She would have no travel costs to factor in either - so does that mean work is very near home? Depending how the working hours occur, childcare could be needed for quite a lot more than the working hours.
If say travel to/from work was around 15 mins, working hours were 9am-1pm, then childcare would be needed say 8:30am-1:30pm to allow for a little bit of time for delays and getting ready to be on the shop floor (in retail jobs they may not pay from arrival time on site but at start of actual work - I have had that happen in leisure industry/theme park, been too long since I did retail to remember exact pay arrangements).
So 20 hours work, 9am-1pm (4 hours) over 5 days would need childcare of 8.30-1.30 for 5 days, so 25 hours. This is theoretical, the working hours are not known at this stage, or how long a gap will be needed between dropping off children/leaving home and starting work. This however does need to be thought about as it increases the cost of childcare.
Then you need to consider taxation.
If she was on £6.50 an hour say, then 20 hours per week that is £130
At that level she has no income tax or national insurance deductions.
Nanny with salary of £10 gross an hour working 25 hours per week, would get gross salary of £250 and there would be Employers NI of £14 per week, so cost to employer of £264 per week.
Payroll needs to be done, could be done by herself but outsourcing it will cost around £150 a year (price varies), so lets say £3 a week in admin cost to try to keep to whole numbers.
So total at this stage is £267. This amount is the figure that could be told to tax credits, as I believe they allow you to include Employers NI and payroll admin.
70% = £186.90 leaving £80.10
There there are other costs of having a nanny such as outings/activities. Toddler groups can be low cost, though some in my area are charging £2 or more. How will nanny get to activities, will that involve cost? If you gave it a budget of £10 a week would it be enough?
So yes, may end up with around £40 a week. However meanwhile nanny has been using heating and electric at the home which may not have been used as much if the children were not there.
It is going to be tight and any changes to tax credits may affect things.
She may be entitled to other benefits, so checking to see what she may qualify for once working could be useful. Turn2Us: Benefits Calculator
A similar calculation would need to be done for a childminder.
In my area childminders charge around £5 per child. Based on 25 hours, that gives £375 per week. That is £75 over the threshold amount for childcare element of working tax credits. So max claim amount would be £210 (70% of £300) leaving £165 per week to pay.
Their income if at £6.50 per hour, 20 hours is £130, so it can't be done.
So establishing likely costs of a childminder is necessary. Family Information Service in your friends area may be able to give details of average costs. They will be able to provide a list of childminders, whom your friend or yourself could contact to find out cost and availability - would they take 3 children under 5 for a few hours per day?
Location can make a difference with childminder costs, it can vary quite a bit. So establish typical cost, so you can either include it as a possible option if you were to find a childminder who would take 3 children under 5 (some may, especially if they are working with another childminder), or rule it out due to cost being too high.