The company I recently started working for had my wrong National Insurance number (off by a digit). I contacted them to get it rectified but it seemingly wasn't rectified in time for my first pay cheque. I've emailed them to ensure it gets rectified for my next pay cheque but my current pay was taxed at the 0T tax rate.
What's the process for getting my tax back? Do I ring HMRC and tell them the NI number it was taxed too and the correct one? Will it get fixed when work rectify it?