Check ID documents. UKBA Summary Guide for Employers on Preventing Illegal Working in the UK (PDF)
Contract - see ACAS: Written Statement for what it must contain.
There are example/template contracts and nanny payroll companies can often produce a contract. Example Contract. If using an example/template contract check it meets the requirements as some may have been produced some time ago.
Agree a Gross Salary.
Probationary period - how long, when reviewed, notice period applicable during probation. This is to make it easier for both sides to cancel the agreement if things do not work out in the initial month or so.
Hours of work. Clearly defined if possible or example given of typical rota for say several weeks.
Holiday entitlement. Minimum is 5.6 weeks There is no right to time off on bank holidays, if you need your nanny to take bank holidays off work as part of their annual leave then make that clear.
Accommodation details if providing. Details of which meals are provided.
Gross Misconduct. I would include in this section things that you feel will result in instant dismissal. Some contract templates say things like: Misconduct which may be deemed gross misconduct includes but is not limited to theft, drunkenness, illegal drug taking, child abuse and violent or threatening behaviour (be it verbal or physical).
I feel that if there is something you specifically would dismiss them for, then you should put what that is so it is clear from the start. This could be things like smoking on duty or on your property at any time.
If it is legal to have a clause like that I don't know but I feel it states the intention of the agreement, so I would have thought that a tribunal would take it into account.