Thanks for your comments, helpful as always! As the time change is only 40 minutes it probably won't be covered by the policy, though. However, I have been able to change the Turkish Airline flight to one only 1 1/2 hours later.

Both BA and Expedia said that the next feasible TR flight was the 1855, but Expedia said that upon trying to book it it didn't exist. TR themselves had a 1905 flight, which they were happy to change my 1730 reservation to.

So the story has a happy ending - or perhaps not an ending yet as I have yet to see if it all works!