london to athens?

[greentea]

hello! i'm planning on going on my first backpacking trip for 3 weeks at the end of august. i'd really like to fly into london, then train on down to athens, stopping at a few places along the way. i really have no idea about how long it takes to get from one city to the next. is it completely unreasonable to go from london to athens in three weeks??

thanks for your help,
katie