HMRC have a webchat service which is very good. I have used it a couple of times to get my tax codes corrected in real-time while I am chatting to them.
Use the link below during UK working hours. Initially, you will be connected to a digital assistant. Ask if you can speak to a human. There may be a wait, but at least it's free and you won't be cut off whilst waiting. You can also save the chat as your record of the "conversation".
https://www.tax.service.gov.uk/ask-hmrc/chat/online-services-helpdesk