Full-time could mean anything from say 40 hours a week to 60 hours.
If 8am-6pm, then let's say nannies wage was £11 gross an hour (not unrealistic for outside London I feel, though you can get a feel for local wages by looking on nanny recruitment websites). So £110 a day. 5 Day working week. 50 hours a week = gross salary of £28,679 per year.
Payroll Calculator
Employers NI: £2982
Payroll admin cost: Varies, lets say £130
Weekly expenses kitty (for activities/outings) - lets say £5 per day, so let's call it 240 working days per year - nanny will get holiday. Kitty = £1200
On top of that you may pay for some more costly activities, such as swimming lessons, music lessons and the such-like... but those are of course very much optional and if you do them you would probably be doing them regardless of having a nanny or not.
So running total so far £32,991
Nannies travelling costs whilst on duty will vary from situation to situation. If nanny uses their own car, then employers would usually reimburse the cost at £0.40 per mile (this is known as the Approved Mileage Rate) - goes up on 6th April to 45p per mile I believe.
How many miles your nanny does will vary. I do quite a lot, around 4000 miles a year so a cost of £1800 a year if at £0.45 per mile.
I don't know how much travelling your nanny would do, so lets add £1500 for travel (which may or may not be reasonable depending on the circumstances), pushing our running total to £34,491
While your nanny is on duty, you give them food and drink. Nannies don't really get a lunch hour, can't leave your children home alone. So food is seen as a sort of perk in compensation for working without a break. How much does that add to your weekly food budget... I'm not sure. Nanny will eat with the children, so eat the same thing. If nanny wants something different, I feel nanny should be buying that themselves. So increase in food bill, extra £3 a day maybe? Heating/Light will also be used more as nanny is around during some of the day, so another few pounds. If comparing with a childminder/nursery, lights wouldn't be on at your home, heating may also be set low.
There is also some additional wear and tear on the property. Shall we lump all these types of cost together... say £2000 a year (about £8.33 per working day). Suppose you could include cost of Employers Insurance in that (as it is part of the home contents cover usually).
So £36,491
Bit of rounding up perhaps... so £36,500 cost to employer for a 50-hour per week live-out nanny.