I have only just realised that the last two posts I had intended for the list were actually sent to Brett Parker by mistake. I wondered why they didn't appear in the list. :-))
The problem is now solved. There was a 'Host' section in the /etc/ssh/ ssh_config file on the laptop which started 'Host desktophostname' and changing that to 'Host desktophostname 192.168.0.1 123.234.345.456' cured the problem. 123.234.345.456 would be the IP address I use to connect, via the Internet, to my desktop at home when I'm away.
I discovered that because if I changed the SSH command to use an IP address, even from my home network, instead of a host name I had the same problem. Brett suggested looking in the ssh_config file 'Host' section.
I'd like to thank everyone who tried to help including ChrisG with his remarkable vocal powers (if Brett is to be believed).