Bill, the * modification was not an "upgrade" carried out on rifles in service. It was incorporated during the manufacturing process.
The only way this would have happened as part of the Weedon programme would have been if a Mk1 rifle was found needing a rebarrel, in which case a Mk1* barrel may have been used to carry out the repair.
Just to show the difference between your MK1* and my Mk1, here's a pic of the breech area on mine.
By the way, mine appears to have escaped the Weedon process all together.