Yeah there are no automated replies to customer service, but look at it this way, if comes to it you're building a record of how difficult they are to deal with.
They will have to issue you with a final letter of complaint or they are obstructing you From taking a case to the financial ombudsman and that is very important, you don't want to be outside the six years doing that. I would try again and tell them that the situation is, you either need them to correct their mistake immediately or you need a final response letter to issue complaint proceedings with the fso. Give them a deadline, 7 days say, and if they do not do it, you will be contacting your legal representative. The key here obviously is that you have to be willing to do that - and then do it if they don't either fix the mistake or provide the letter
I had a similar situation with them in march over confirming review and was promised a call back by someone more senior which didn't come, did this, and had a call with in a few hours, now i still ended up going to the barrister, as the more senior person was entirely unhelpful, but the threat got someone on the phone.
Your other option is to forget fso and if you are sure you have a case just sue them for breach of contract, ie they failed to fulfil the condition of your contract whereby they promised you a particular interest rate but either way you've got to start one of them before your six year deadline is up. It is highly possible that the bank are dragging it out to take you outside this limit
A third option is to file a complaint with the fso saying you can't get your final response letter