Not sure there is a list of things.
Employment law advice can be found online from ACAS.org.uk and AdviceGuide. Taxation information is available from Gov.uk and HMRC.
Immigration checks info is available from UKBA.
Pay level - look at what others are offering in the market. Sites like Nannyjob.co.uk are useful for looking at nanny job adverts.
Agree a Gross Salary. Do not discuss Net (take home pay) as the person will have other income on other days and you have no idea what their individual financial circumstances are.
Talk to a nanny payroll company such as PAYEforNannies, ZestPayroll, NannyMatters, NannyPAYE, NannyTax to discuss how they can help you with the payroll if you do not fancy doing it yourself. They may also offer additional services such as Contract Writing and Employment Law Guidance.
Nannies work a variety of hours, some may do 5 hours a day, others may be 12. Advertise for what you need. Some nannies start very early, some finish very late.
Consider where someone will be living... how long would their commute be, how will they get to you - is car the only way. Do they need to drive as part of the job, will you provide a car or do they need to use their own. Is their car large enough to transport all your children?
You can have as much or little control as you like. The amount of control may change over time, initially you may want to dictate things but once you trust the nanny to just get on with things you may simply say that x, y z need doing.
One day a week is not much time to do many household tasks. If you want a cleaner, employ a cleaner. A nanny may stick a load in the washing machine, put the dishwasher on but that's probably about it when in a 1 day a week job unless there is a lot of child-free time.
A nanny gets paid holiday. 5.6 weeks is the minimum. Depending on their day of work there could be a lot of bank holidays (Mondays in particular cause a problem in this regard). Decide if you want your nanny to work on a bank holiday - make that clear at interview stage. Remember that Xmas and Boxing Day vary their day of the week, so even if nanny is not working on a Monday, they may still have a bank holiday some years. More about holiday entitlement is available from Gov.uk and ACAS.
Your nanny is there to care for your children but also there to make your life a bit easier. So don't be afraid to ask them to do something - you are the boss. Just be reasonable in your expectations, their primary role is care of children not to be your PA, Cleaner, Plumber, Electrician, Pest Exterminator, Chicken (and other livestock) Keeper, Dog Walker etc.
Make a list of the things you would like your ideal nanny to do.
Keep in mind that children grow up quickly, a napping toddler now won't be napping in 6 months, a year... at some point daytime naps get dropped. Their needs change, they become more active and need mental and physical stimulation.