Your tax code is 647L but you don't get to earn that up front before paying any tax. You get it in incremental steps. If you are paid weekly then you will be taxed on anything earned over £124.50 in the week (or cumulatively anything over £124.50 x the week no. you are now in). If monthly then anything over £539.58 on the same basis.
Presumably you've earned more than than if you are being taxed so far? Your tax code has nothing at all to do with national insruance. You'll pay that if you earn more than £110 in any given week regardless of cumulative figures or tax codes.