Mail failing to send messages

I have a problem with the Mail Application.  I can receive mail, but cannot send.

I have 2 Imacs

I am using version 16.0 with Ventura 13.4.1 and:

Version 11.5 with High Sierra version 10.13.6.

My ISP is Virgin Media.

I can send and receive emails if I use my email facility on the Virgin Website. 

When I do attempt to send using Mail I get the message that Virgin Media is offline. It shows “offline" in the “accounts" tab of System Settings.

It asks me for a password and will not accept the one  from my account settings or any alternatives I provide. 

Using the Connection Doctor has not worked.

The virgin Help line say they can install an over ride programme for approx £20 and a monthly charge of approx £5 thereafter. This seems like a scam, especially as I have been using Apple’s Mail programme for about 30 years without a problem.

Can anyone offer practical suggestions to get over this problem