Eurostar + TGV or IC takes 7 hours with a change in either Paris or Brussels (I’d choose a route through  Brussels).   Schedule time at http://reiseauskunft… is 6 hours due to the time change, as London is in a different time zone so you lose an hour.

Whichbudget.com doesn’t show any direct flights on cheap airlines. Mobissimo shows some flights from Gatwick which aren’t too expensive.   Flying, with time to get to Gatwick, will probably take 4 1/2 hours to 5 hours — longer if there’s any kind of security slow-down.  Flight time is just over an hour, so schedule time looks like 10 to 20 minutes.

Thanks for the info:
 
First Option: Through Paris – I am trying to look into the schedule and it dosn’t seem practical as the stop over is about 8 hours in Paris.
 
Second Option: Through Brussels – I cannot seem to schedule through Brussels. Perhaps you could just point me the steps of what you did.
 
In between 6 hours on the train or 5 hours on the flight, I would prefer to see the countryside on the train. Let me check.

I just filled in London and Luxembourg Gare in the schedule at bahn.de.   I was using a weekday and departures starting at 8:00 AM.  The initial search shows 3 choices — 2 via Brussels at just under 6 hours, 1 via Paris at just over 6 hours.