There a number of hotels in the area surrounding Imperial but they will fill up fast at this time of year. I would encourage you to book as soon as you are able to confirm your travel arrangements.
My suggestion would be :
The Grange Strathmore (4*) 41 Queens Gate Gardens, London, SW7 5NB - just a few minutes walk from Imperial and off the main roads link
At the time of writing, a single room is £120 / night directly from them, including breakfast and wifi.
Once that is full, there are plenty of alternatives - try one of the generic sites, looking at the south kensington area if you want to be within walking distance e.g. booking.com
Here are some options picked out from that - there are currently rooms available that are of a similar price to those above but you can certainly find something cheaper if required (if using booking.com look at the prices buttons on the left-hand side of the page) :
Citadines South Kensington (4*) 35A Gloucester Rd, Kensington and Chelsea, London, SW7 4PL - again, very close to college, a busier road - this is an apartment hotel link
Fifty four boutique hotel (4) 54 Queens Gate London, SW7 5NB - very close to college link
Radisson Blu Edwardian Vanderbilt Hotel (4*) 68-86 Cromwell Road, Kensington, London, SW7 5BT - again, very close to college, a busier road link
The Queen's Gate Hotel (4*) 31-34 Queen's Gate, London, SW7 5JA, United Kingdom - a little further but eminently walkable and very nice (and commensurately a bit more expensive) link
Hotel Mercure London Kensington (4*) 1a Lexham Gardens, Kensington, London W8 5JJ - again a little further but still walkable in my book (circa 15mins, I would guess) link
Should you require more luxurious surroundings then I would suggest : link