Sky Europe have flights into Athens from Prague and Krakow, which are both reachable from Newcastle with Easyjet. They (Sky Europe) also fly into Athens from Budapest, Bratislava and Vienna. Think you can also get Sky Europe flights from Manc land to Bratislava and Krakow and also to Salzburg (train on to Vienna). Their website is slow as fuck though.
http://www.whichbudget.com/en/cheapflights.php?to=ATH
Thats Which Budgets list of carriers/countries flying directly into Athens. You can alter it a bit if your wanting to land somewhere else in Greece and train it to Athens.
You should certainly be able to do it for under £200 if you have a weeks worth of travelling time. Lots of German options available as well which should all be reachable from the UK cheaply.