Hard to know nanny salaries in Scotland as there are not that many jobs advertised. Looking at online job listings, £8-£10 gross per hour seems typical.
So... taking £8 gross per hour, 41 hours = £328 a week/£17,103 per year. Employers NI currently adds on £1458 (this amount will vary as NI rates change), so you are up to £18,561
You then have the added cost of activities, nannies mileage (if driving children around), cost of food, heating, electrics etc.
As you are in Scotland, to use Tax Credits or Childcare Vouchers you need to hire the nanny via a Nanny Agency. Some agencies offer a service which enables you to hire a nanny yourself, then just use the agency for registration purposes. So going for the lowest cost option, I think that would add another £150 say.
You could do payroll yourself, or use a payroll company, say another £130-£150 for that.
I am very surprised that a childminder can provide childcare for 3 children, for 41 hours a week, for £150. That figure in my mind must be wrong, there is something you are not telling us. Maybe you mean £150 per child. Maybe you mean £150 plus whatever you get from tax credits (think max from them is £240).
A nanny I feel will cost you £400+ a week.