I do a 40 hour week over 4 days. I'm paid Gross, so doing some calculations, my Net pay is around the £300 per week mark. Thus your £340 Net sounds about right, for an experienced nanny working in the South East (particularly London, where rates are a bit higher than I get in Berkshire/Surrey).
A word about Holidays. The entitlement has changed over recent years. Now that your nanny wants to do the hours over 4 days (is that right?), calculate how many days holiday your nanny can have using the Holiday Calculator.