I have just received the following further response.
Our logs are not showing any failed SMTP access to your account (xxxxxxxxx) corresponding to the mentioned date. This seems to indicate that the client is not correctly connecting to our servers.
Its also likely that you are mixing up SSL/TLS or port 465/587. What I would suggest is testing SSL with 465 as well 587. See if one of those works.
If they have thoroughly tested with both SSL and TLS on both ports, then the only other explanation is that they are blocking/fire-walling the ports. In that case, you need to get in touch with your host and ask them to allow the ports.
I am right now going to check both ports.
Rather than simply checking them myself, I will get the ISP to check them for me, in case I am doing something wrong.
(After all, the weakest link in the chain in all of this is likely to be me, and I am aware of that!!)
With every good wish,