I'm thinking that there may be an issue where the site doesn't show the drop down to change your seat if the first leg is not Virgin Trains East Coast, even though subsequent ones are. However it may still be able to access this page.

Try the following steps.

  1. Log into virgintrainseastcoast.com as usual
  2. Go the the My Bookings section
  3. In the drop down select Amend Journey (assuming Amend Reservation is not available)
  4. In the address bar change the first part of the URL before the query string (that's the question mark and following text) to:
    http://tickets.virgintrainseastcoast.com/ec/en/purchase/AfterSaleActivit...
    So for example if the URL is https://tickets.virgintrainseastcoast.com/ec/en/account/OrderHistory?_ga... change it to 
    http://tickets.virgintrainseastcoast.com/ec/en/purchase/AfterSaleActivit...

Let me know if it works.