Personal Tax allowance on two pensions

I have recently received my state pension, and also receive a CS pension. I was dismayed to learn from HRMC that I have been given an emergency tax code and that my personal tax allowance is now being used on my state pension which was previously used on my CS pension. This has led to me paying far more tax than anticipated and my monthly income, sadly, nowhere near that which I anticipated. Can I ask HRMC to use my personal tax allowance back to my CS pension, which is greater, and pay tax on my state pension?

Hi,
You will need to contact our Income Tax team to review your tax codes and allocate accordingly.
Income Tax: general enquiries 
Thank you.