As from 1st May 2015 British Airways will fly from Heathrow to Corfu every Thursday, Friday, Saturday and Monday.
http://www.thetoc.gr/eng/food--travel/article/british-airways-to-add-routes-to-corfu-and-kos
And the prices are VERY competitive, take a look on line, and bag a bargain!
Their prices are seriously worth a look. On my dates for next year I would've saved £120 if only they flew direct from Manchester. The flight timings are more than good and you get 23kg hold luggage at about £20. I've flown them before, the cabin crew were brilliant; force feeding me free food and Bloody Mary's! So different from my Jet2 crew this year who were having arguments with each other under their breath.
Just checked the same flights again and the prices have doubled!