Does this happen when using webmail, or an email client? Is this only at home using VM internet connection? What if you turn the internet/wifi off and try data, or go to another location and use wifi? The reason I ask is that recently there are quite a few customers with blacklisted public IP addresses.
If you can get the error code from your email client, the superusers can confirm this or advise appropriate action if a different error code is presented.
@shrek ok a very, very quick and dirty check for something.
Just looking at your phone to start off with, I take it that when you are at home, it won't send any emails, am I correct? Just some error message about passwords or accounts?
If so, if you take the phone somewhere else so it is not connected to your home wifi (or alternatively stay home but turn on the wifi on the phone) what happens then if you try to send an email from it?
Report back the VM3xx error code from the Thunderbird log and the result from the IP check in Spamhaus and what blocklist the IP address might be on. Some blocklist listings don't matter but if you are on SBLCSS it matters a great deal. The check will tell you that.
No other way through this. We have to diagnose.
As a Very Insightful Person, I'm here to share my knowledge. I don't work for Virgin Media.
I'm going to bet good money that it won't last and you'll find yourself unable to send emails within a few days or so. When and if that does happen, please follow the advice of @HowardML avove regarding finding out your public up address and putting it in the Spamhaus check box on the link he provided.
Also, and this might seem like an odd question, when you went away, what devices did you take with you and did you leave anything behind at home still plugged in and working i.e. Aamzon Firesticks, Chromecasts etc?