Ok, for starters, the Eurail does not cover the UK (and not to mention that the UK is crazy expensive cause of the pound.)
With 20 days and your itenary, I would look at useing the Eurail and a low-cost flight like ryanair.com or easyjet.com
If anything use the flights to go to and from Greece. Book as far in advance as you can to get the best prices. I have never flown Ryanair, but I have flown Easyjet many times, and I can say it is just like flying Delta or any other airline for the most part. So it's not like you are sitting on a chicken coop in the back or anything like that.. And you can't beat the prices..
Have fun!