Well, in the end I emailed Ancestry's customer support and I must say I'm very impressed - they got back to me so quickly and it was such a simple fix - even if I would never have discovered it by myself!
So, in the hope it might help anyone else in the future - here's what they said the problem was:
After reviewing your account, we noticed that there are a few relationship errors in your family tree that are effecting both Thrulines from showing correctly and the ability to turn on the Thrulines icon in your tree. For example, your parents are not listed as your biological parents in your family tree; the relationship is set to "Unknown." In order to fix this, navigate to your profile page, click "Edit" in the top-right corner and select "Edit Relationships" in the drop-down menu. There are a few more "unknown" relationships that we recommend fixing in order for Thrulines to show correctly. So who'd have thought that clicking "add father/mother" wouldn't automatically make them biologically related to their child!
But anyway - the DNA Discoveries "ThruLines Icons" toggle is now "on" and checking with ThruLines I can easily see which ancestors need fixing as they gradually change from green to pink/blue!!
Thanks for your help and listening ears during my misery!
