I would not trust that information. The Employment Status manual is huge and any one factor alone does not determine employment status. So how Gov.uk can say that is beyond me.
Are you deciding how much to pay?
Are you deciding when they do the work?
Are they able to say no to coming into work, such as offering a different day instead (which is what a cleaner would do)?
I would view them as an employee if the hours are set and regular.
If it is more like ad-hoc babysitting then that would I feel be different.
Whilst HMRC might allow a nanny to be self employed, does the nanny want to be self employed? Do they want to run their own business, not have entitlement to paid holiday or other statutory rights? Do they want to be doing accounts and a tax return?
Do you want to stop another person (probably a young women) from having employment rights - things that women especially have campaigned for years to get?
At 10 hours a week there is unlikely to be any Employers NI. So costs you need to consider are things like:
Payroll Admin (£140 a year, or do it yourself)
1% employers pension contribution (might not be until 2017/18)
Statutory Sick Pay (don't think this can be claimed back as it could in the past).
Yes it is a pain being an employer but it gives the worker more rights and you have more control over what they do, when they do it.
Hard to tell someone who is their own boss what they should be doing!