Problems Closing American Express Account

I have just tried to close my American Express account. Apparently nobody at American Express' UK head quarters in Brighton is trained to close accounts. I tried to explain to the poor agent on the phone that she should get a supervisor but they're not trained to close accounts either. Or, when I asked, was their boss. And there are no escalation procedures in place to deal with the problem.
To me it seems another obvious ploy to stop people closing accounts.

American Express Dispute

I've just got into a dispute with American Express. I was a day late making a payment of £403.75 against an American Express Platinum credit card. They've charged me £23.52. By my reckoning that's 5.83% for one day!!! On an annualised interest basis the charge is preposterous. Even if I ignore the £12 late payment fee, the interest fee is still £11.52, which works out at 2.85% for 1 day's delay.

This is the first time I've missed a payment with them. Needless to say I have told Amex I'm cancelling their card. Obviously American Express must factor in the sort of response I've made. Good luck to them. They won't get my custom ever again.