EU passport holder means nothing to Turks. You have no shot at making this connection and you'll have no protection unless this was booked on a single reservation (which I gather it wasn't). Is this transfer to international or domestic? If domestic you may be able to claim your bags at your final destination provided you can get them to check it through all the way. If going TK to TK this may well be possible. If by some miracle you park at the gate (as opposed to remote parking) by t-45 you "may" make the connection.

I always try to book my domestic connections about four hours after my arrival as there is usually a good chance they can accommodate me on an earlier flight once I get to the checkin at İstanbul.