Thanks for the reply. Your username suggested you might be in the North East, so I particularly looked for routes from there but I couldn't find anything.
Your ideas don't seem to be viable because there are no flights from Newcastle to Bucharest, Vienna or Frankfurt:
http://www.newcastleairport.com/FlightInformat ion/Europe.htm
(There aren't any flights to Iaşi from Frankfurt anyway).
Your easiest route is probably with Austrian/Tyrolean Airways from Edinburgh, via Vienna. Unfortunately the Austrian Airways website doesn't offer through ticketing for that journey, so you'd have to contact the airline to see if it's possible.
Confirmation that the only route into Iaşi are via Vienna, Timişoara, Budapest and Bucharest can be found by checking all of the available flight schedules on the Iaşi Airport website:
http://www.aeroport.ro/index-eng.htm
(It won't take you long; the airport only receives a total of 7 flights each day!).
I've taken another look at the Thomas Cook Rail Map and realised I was incorrect when I stated that there are no rail services to Iaşi, but unfortunately most alternative airports are a very long way from Iaşi. The only ones reasonably nearby (with rail connections) are Suceava, Bacau and Chisinau (across the border, in Moldova). I'm not aware of any flights into Suceava or Chisinau which might help you but (if you can get to Luton) you could get a flight with Blue Air to Bacau, and then take a train:
http://www.blueair-web.com/index.php?LANG=EN
Chris