Well, yesterday was an expensive day.
Firstly, neither my RAC cover nor my home insurance include key cover.
The Replacemykey website didn't respond to my reg. number.
So, I bit the bullet, and after a final search phoned the Fiat dealer. I then went over there with V5 and ID, and ordered another key. This comes from Italy, takes 7 days and costs an eye-watering 261.70. When it arrives, I go there and they reprogram my remaining key and the new one. This costs a further 50 quid. If I ever find the missing key it will no longer work, but could be reprogrammed to become a second spare.
The guys at the garage couldn't have been more helpful, courteous and sympathetic. Obviously there was no point in ranting at them about the cost, but it is outrageous, even if it is self-inflicted.
Presumably they will cut the emergency mechanical key to match.
Oh, and thanks for the link, Goodcoin, but that key is different to mine. No PANIC button on my key, although it would have been appropriate when I found I'd lost one!