Salarycalculator.co.uk is very accurate.
Personally I would recommend still holding private insurance (most companies offer it). The few things my family has needed (allergist, dermatologist, dentist) are not covered on the NHS (well, some dental is but it's very bare bones).
£30k would be take home of £1,950. £35k would be take home of £2,240. Most people are paid monthly here.