I have never flown T. Cook airlines, but have read MANY reports by those who have ... you won't find them on R. Steves forum, because mainly the passengers are from UK, often travelling on a "package holiday" deal. T. Cook packages can be bargain-basement with thus predictable glitches; same goes for Ryan air, which has tempting lo prices, but then charges for everything but the air u breathe. Also, there are many complaints by people on these 2 airlines about snafus & terrible crowds at Santorini airport, mainly upon leaving, but also on arriving. NOT the way to start a relaxing Greece vacation.
I'm not sure why the travel agent suggested London/T.cook when there are MANY European airlines that fly direct to Santorini. Friends of mine recently were in Italy, and got a great flight from Rome on Aegean about 10 AM, arr Santorini 11:30. And why stay overnight??? There is NO need to -- and the costs for staying at a London airport hotel would wipe out any savings from a bargain ticket.
I would worry about this travel agent on this score, and on another -- is he/she the one who recommends visiting Santorini midweek?? I always (from experience) recommend the opposite -- try to visit Santorini F-S-Su & Mon at latest. The very heaviest tourist-trafiic from those MegaCruise Ships is worst on T-W-Th. SO bad in fact that islanders themselves have rebelled, they say the overcrowding is degrading the environment, air water and the experience. Just 2 weeks ago announced a new law capping the amount of cruise visitors per day at 8,000 (8,000!!!). I cannot explain the crowd situation created by this number. When you visit on F-S-S, by contrast, there is seldom more than 1 cruise ship, tho of course many many tour groups arriving by ferry daily.
Since you have TONS of time, I recommend you try some other options. Your aim would be to find flights tat are direct across the Atlantic and arrive in a Major European City in the AM, between 6 - 10 am, and then a 2 hr layover (NOT less, important), and a Flight to Santorini arriving by 2pm or so. If you don't find something you like -- either too pricey, bad times, and/or too many stops, it's time for search #2. I suggest you go on KAYAK and put in some "dummy dates" for your travel, arriving say on a Friday, with airports Chicago & Santorini -- see what you get. Another technique wold be to put in Chicago-Madrid Chicago-Amsterdam Chicago-Frankfurt, Chicago-London, Chicago-Rome. Then go on SKY-SCANNER, a VERY good site for European flights, and put in ___ - Santorini. Aegean has flights from all the major cities and is a SUperb airline ... new planes, top reviews, voted best European airline numerous times.
OR -- if you are using this Greek travel agency challenge THEM to do this. say when you want to go, when arrive etc. BTW, it would help all travelers if you'd say which agency.. There are 2 that are widely recommended on these forums for Americans & Canadians to use, and lately I've heard iffy reports about one of them not being responsive to expressed wishes.