4 days off on October, so where can I set up my luggages ? Not so far because of my limited budget.
By looking at Easy Jet's Website (Low Cost airline carrier) I found some Lyon/London return tickets very affordable: 75€/pax (seen 2 months and a half before the departure date).
I bought 3 tickets without taking care of accommodation.
Flight: Easy Jet for Lyon (LYS) / Londres Gatwick (LGW) trip.
Accommodation: the cheapest solution was booking a room by AirBnB. They provide bedroom from local people. I found mine for 80€/night for a 4-person-bedroom. The owner had quickly answered to my questions and seems to be nice and helpful. Her house is next to a subway station.
Moving: I booked a shuttle from airport to the city centre with Gatwick Express. It costs me 90€ for 3 return tickets, but I will save time instead of public transport. For tourism movings into London, I will buy a subway card during my stay.