Assuming you’ve checked all your settings are correct….
I’m with Talk Talk for email and had the same problem. They (TT) don’t allow access to their SMTP server when not on their network (I.e. when sending email from my phone via O2 in my case).
In Android, I needed to change the Outgoing mail server settings to my O2 account settings so I send outgoing email via O2 servers and receive via TT’s servers. something like:
SMTP Server: smtp.o2.co.uk
User name: yourname@o2.co.uk
Password: yourpassword
If you’re not with O2, you’ll need the smtp server settings for the provider you’re with.
The pop3 settings can be left with your BT credentials.