|Hi again, I did as you suggested.|
I changed gateway in second router.
I switched off DHCP in both routers and manually assigned IP addresses in each PC.
I also had to assign DNS addresses, even though though the router was set up to assign them automatically. I don't understand that bit.
I am pleased to report that the setup appears to work as required.
I have tested it at home where I have only one ADSL line, but it appears that a host can only connect to the internet if its router is connected to the line. In other words, there is no internet traffic through the cross over cable.
Also, it is possible to share the printer.
Thank you very much for your help, I would not have been able to do it without it.