Thanks for your account of the process, it's very helpful and prompted me to contact Amex for an upgrade myself.

I spoke with customer services last week, and they verified my eligibility for the Centurion card based on my spending on my existing Platinum card and said that they'd get somebody from the Centurion team to call me back. I heard back the next day and the person who spoke to me asked me (a) if I am aware of the £1800 annual fee and (b) if I have an annual income in excess of £200k. Yes, to both, so they have passed my details to the Centurion invite team and said that I should expect to hear from them within a week or so.

Just one quick question for you: what do they ask for in terms of proof of income? My financial affairs are complex, and I don't have payslips as such, although I do have bank statements backing it up...