I'm afraid that your former employer/current pension payer is being somewhat intransigent.
Most PAYE tasks are handled online now and there is a learning curve for everybody. As you have told them that your tax code has changed, they really should contact the tax office on the phone to confirm the change if they haven't received the P6 online. As they are using an 0T tax code instead of the 350L tax code, you are having too much tax deducted assuming that the 350L code is the correct one. When you retire, there should be a smooth transition of your tax code to your pension and as both your salary and pension have been operated by the same people, there really should not be any problems.
If I were you, I'd tell your former employer that there are penalties for employers who operate PAYE incorrectly. Take a look at the notes here
. They mention using incorrect tax codes which have been superseded by electronically issued codes. HMRC have a record of codes issued electronically so even though your former employer may be able to show that the revised tax code was not received, the fact that you have told them the code has changed really makes them obliged to check it out. If there is anybody in authority at your former employer you can speak to other than the payroll people then I'd suggest you try that before contacting HMRC again.
If your former employer refuses to contact HMRC, you can ask HMRC to contact them as it says in the notes. If HMRC refuse to call your former employer, then I would escalate the matter into a complaint. You can read about that procedure here
. The complaints managers are usually quite good at banging heads together and sorting problems out. There is no excuse for both of your former employer and HMRC doing nothing.
I hope this helps but let me know if you have any further questions.