As of 06.30 am today 1 Jun 2007, test e-mails arrived at their destinations promptly. It seems the ISP is getting it's act together. Their website claims that test transmissions to all major ISP are now OK, with the exception of AOL.
It is disappointing that this turned out to be a non-event, in the sense that there was no technical problem to chase down and resolve. It was pleasing to find that Pegasus Mail was blameless.
Finally, it was nice to discover this forum, and come away with the comforting feeling that any future problems are no longer likely to be major obstacles.