As a nanny, I can say that I don't feel it is normal for a nanny to be taking very many days off sick. I can't even recall having a sick day in the last 3 years. Had a funeral day, but my boss insisted I had that day off.
Typical nanny contracts state sick pay as being SSP... thus an incentive for the nanny to be sick. Employers than can pay for sick days at their discretion - and of course stop paying after a certain point, or if they feel that the sickness is not genuine.
MrsFogi - if you can, try stopping paying for sick days (check to see how contract is worded). Do return-to-work interviews, so that there is a written record of the sickness - so you can refer back to it in future, may also help establish if there is any pattern and if sickness is genuine. Discuss the amount of sickness your nanny is taking with her, and if you feel it is necessary give a verbal warning that if sickness record does not improve, then a written warning will be the next stage in the disciplinary process. Too many written warnings, and contract gets terminated.
Sickness At Work - Advice for Employees
This contains details about an HMRC service called Medical Services, who can do a report with regard to if the employee has been off for good reason, or not.
Absence Management Toolkit - For employers, to help manage absence. Aimed at small businesses, but worth reading as you may find some of the suggestions useful.