RFCC,
It might be a DNS (Domain Name Service) problem.
I'm assuming that your mail server with ISP-1 is an "intranet" service - that is, your PC and the mail server are on the "same" network, not the public internet.
So you
can resolve names on the intranet, but not the internet - e.g. ping smtp.myisp.co.uk resolves to an address such as 192.168.12.10.
Try pinging your email server, then try pinging
www.bbc.co.uk.
Next, check your IP configuration with ISP-1 go to a command prompt, type ipconfig /all. In the listing should be entries for DNS server(s). If there aren't any that's the problem. If there are DNS servers and you get a response from pinging bbc, then it may well be a browser or firewall setting.
Have you got a proxy set up for ISP-2 that you don't need for ISP-1?
Try disabling the zonealarm firewall (briefly) for a short test to see if you can connect.