You can't equate nannying with cleaning at all. One is a self-employed job that involves hard physical graft, and consequently there are only a limited number of hours it is possible to work each week or you would keel over.
Let's think about this. The vast majority of cleaners work between 10-25 hours a week in school hours and not a great deal during school holidays. Cleaning also involves unpaid time driving at your own cost from one appointment to another. There isn't a cleaner on this earth that works at full throttle plying his/her trade in one person's house for 50-60 hours a week as nannies do, with sick pay and holiday pay all covered. Also, £10 an hour for a physically hard, time-limited freelance job of this type equates to something like £7 an hour with no additional superannuation costs to the employer. Most cleaners are lucky to take home £10,000 to £12,000 annually and would owe about £2000-ish in tax on that, I reckon (whether it gets paid or not is a different question, of course).
Nannies, on the other hand, are almost always employees. That means that their employers have to find an addition 35% or so on top of the net wage in superannuation, and in addition to this there is the employer's national insurance contribution which in a year comes to over £1000. Nannies also receive sick pay and something in the region of 6 weeks holiday pay a year. Many of them earn roughly £20,000-£25,000 gross, which makes the salary approximately double or even triple that of a cleaner, when you take everything into account, even if they are trying to say rather that cleaners are earning more than them per hour (which is inaccurate and utterly irrelevant).
Lawyers are in a different category altogether. The £100 an hour you might shell out to see one also includes some time spent organising and researching your situation, and also the overhead costs such as an office, administrative staff, membership of the Law Society, continuing professional development, access to online law databases, maintaining the parking space you use when you visit them, and so on. Again, a lawyer is not seeing clients for 50-60 hours a week at full throttle. Neither is the fee the lawyer's personal money, it is a fee for professional services. What the lawyer will take home at the end of the day is often quite unrelated to this (some solicitors will be earning less than some nannies, particularly if they are doing a lot of legal aid work as well as seeing private clients for their firm, for example).
It would be much more sensible for nannies to think of their salaries in terms of annual amounts of money as the rest of us do, then they would see that their salaries are around the level of the national average wage. Comparing hourly rates with freelancers and attempted to claim that this is 'fair' without taking superannuation into account is just plain daft.