I was considering taking a coach bus as an alternative cheaper form of transportation, in addition to seeing Europe by road.
It's not worth it. You won't even notice which country you're in. Plus, it's a thirty hour trip, and a good deal of it will be at night.
If you do take the coach. Stops are every four hours... for about 15mins.
The last thing you want to do is lug luggage across London, wait for a bus and then put up with a cramped seat.
Don't forget: there is no left luggage office in London. So it might be a struggle.
Let the airline transfer you and your luggage.