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Most ISPs block access to their outbound (SMTP) mail servers unless you are connected to their broadband or dialup service. This is an attempt to restrict the abuse of their servers for sending SPAM. If only their customers can connect to the SMTP server then its easy to identify and deal with any people abusing it.
If you get an error similar to the following then its the other ISP blocking your access to their SMTP server
An unknown error has occurred. Account: 'ANOtherISP , Server: 'smtp.anotherisp.co.uk', Protocol: SMTP, Server Response: '554 Sorry, your non-local IP address (89.1.1.1) is not allowed to send email via me.', Port: 25, Secure(SSL): No, Server Error: 554, Error Number: 0x800CCC6F
The solution is to set up an "unpaired" account with the POP3 details being your other ISP and your SMTP details as TalkTalk's as detailing in the article TalkTalk Email Settings.
This will allow you to send through the accessible TalkTalk SMTP gateway while downloading from your other ISPs POP3 gateway.
Solution taken from TalkTalkMembers Forum article Can't send e-mail when using another ISPs e-mail account.