During Winter Athens is the only gateway into Corfu so you need to fly there first. Being based at Manchester the only direct flight from MAN to ATH is with Olympic 3 times a week, its a horrible flight, goes at nearly midnight and arrives at 430 in the morning when the transfer is at 500 so you always miss it and end up spending half a day in Athens airport, its nice but not that nice.
To try and avoid this I let the computers here churn out some routes, the best being Manchester to Zurich then Zurich to Athens with Swiss Airlines and then Athens to Corfu with Aegean. While not necessarily the quickest route, the flight times are good, I should be in Corfu at 1900 leaving Manchester late morning and the transfers are all guaranteed and of a reasonable time (1-2 Hours), with my airlines concessions it was also very good value and not much more than £200 at full price, I did book early though.
Obviously with three flights you takes risks with delays, that’s why the computers decided for me to transfer at Zurich instead of Amsterdam as the airport is smaller and travelling in December may be quite funky with the weather but its all character building and I'm in no rush. It’s all a little easier if you live dowe south as BA operate London - Athens quite regularly and Easyjet also do the route but it can be very expensive.
The most fun way if you have the time is Ryanair from Liverpool to Venice and then the Ferry from Venice to Corfu, its very relaxing and highly recommended if you have the time, it takes over a day.