We found a place called "Queens hotel", which is a pretty cheap and well rated hotel for groups of students. It's very popular.
Although we have to take the tube to get to the city of London, this was the best option we could find on different sites.
The total price for four days for 18 people is €1569, which brings the price per person per day to only €21.80.
Each student (and teacher) will pay €87.20 for accommodation on this trip.

