At the private nursery we use, we pay for 51 weeks of the year. Our bill is paid monthly at the same amount, ie: £357 per month (£84 per week x 51 weeks of the year divided by 12 months). This then incorporates the free week per year. I know County Council nurseries are completely different though but you have to incorporate breakfast club price and after school club price as well, if you require care outside normal CC nursery school hours. Also holiday club price when N school is closed.
Don't ask me how the free session pricing works out when the child is entitled to it though, ie: first term after they are 3 years of age - I'm still trying to work it out!!!