Tax underpayment through PAYE

I have just discovered that my PAYE tax code has been incorrect for the last 6 years and I have been underpaying tax that entire time. I am a higher rate tax payer (or at least should be), but have been taxed at basic rate all that time. In my last pay slip my PAYE code was adjusted, but I have as yet received no contact from the inland revenue either regarding the new tax code or the tax that is owed. I work for a large company, which has supplied P60s (or employer’s equivalent) and P11Ds to the inland revenue at the end of every tax year and nothing has been picked up until now. I now know that checking my tax code is correct is my responsibility, but had assumed (rather naively) that your payroll department looks after all matters of tax. I will not make that mistake again. So, I am looking for advice about what to do next, plus if any one has any experience of Extra Statutory Concession A19 and whether they think this would apply in my case? Thank you.