The following day, I dug out all my foreign money, and tried to get this changed at the banks. I found out though that I needed to have my passport with me, and as the banks closed early, I didn't have time to go back and get it.
I tried my other bank card at an ATM and got a different error, indicating that the transaction had been blocked, so I called up the card companies and found out that both had been blocked.
The original had been due to the fact I'd been trying to take more than the maximum daily amount (which was only £100!), and the other because they didn't expect me to be in Taiwan.
After getting that sorted out, I managed to withdraw money again finally, and then had to move rooms due to a large booking arriving taking up the main dorm.
For the inconvenience I was offered a room to myself :-)