A list of budget accommodation that receives at least 4 out of 5 rating on TripAdvisor. I have not included chain hotels. However, most of the central London Premier Inns are well rated. Check the Premier Inn website for prices and locations.
KING’S CROSS AREA:
Alhambra Hotel [quad]
Crescent Hotel
http://www.crescenthoteloflondon.com/
Euro Hotel [quad]
George Hotel [quad]
http://www.georgehotel.com/english/index.html
Harrison Gastro Pub
Jesmond Dene Hotel [quad, quint, apartment]
http://www.jesmonddenehotel.co.uk/
MacDonald Hotel [quad]
http://www.macdonaldhotel.com/
Studios 2 Let [studios]
http://serviced.studios2let.com/
BLOOMSBURY AREA:
Arosfa Hotel [quad]
Arran House Hotel [quad, quint]
http://www.arranhotel-london.com/
http://www.imperialhotels.co.uk/bedford
Jesmond Hotel [quad, quint]
http://www.jesmondhotel.org.uk/
Morgan Hotel [a/c]
Ridgemont Hotel [quad, quint]
http://www.ridgemounthotel.co.uk/
Thanet Hotel [quad, quint]
PADDINGTON AREA:
Falcon Hotel [quad, 2 room family suite]
Hyde Park Radnor Hotel [quad]
http://www.hydeparkradnor.com/
Hyde Park Rooms Hotel [family room]
Mandalay Picton House Hotel [quad]
http://www.mandalayway.com/hotel/index.html
Rhodes Hotel [quad, quint, frig, a/c]
Tudor Court Hotel [quad]
http://www.tudorcourtpaddington.co.uk/
Winrose Hotel
http://www.winrosehotel.co.uk/
LANCASTER GATE/BAYSWATER AREA:
London House Hotel [quad, 2 room family suite, frig, a/c]
http://www.londonhousehotels.com/
Lancaster Hall Hotel
http://www.lancaster-hall-hotel.co.uk/
Kensington Gardens Hotel
http://www.kensingtongardenshotel.co.uk/
Royal Court Apartments [apartments]
http://www.royalcourtapartments.co.uk/
202 Apartments [apartments]
The Cleveland [kitchenette, a/c]
[Note: I believe it is a minimum 2 night stay, enter your dates in the reservation page to see the rental rates.]
http://www.thecleveland-hotel.com/
Space Apart Hotel [kitchenette]
http://www.aparthotel-london.co.uk/
Vancouver Studios [kitchenette]
http://www.vancouverstudios.co.uk/
MARBLE ARCH AREA:
Parkwood Hotel
http://www.parkwoodhotel.com/ [2 room family suite]
Lincoln House Hotel [quad, frig, a/c in some rooms]
http://www.lincoln-house-hotel.co.uk/
EARL’S COURT AREA:
Amsterdam Hotel [quad, apartments]
http://www.amsterdam-hotel.com/
Base 2 Stay [family rooms, kitchenette, a/c]
http://www.base2stay.com/kensington-london/the-hotel
Twenty Nevern Square
http://www.20nevernsquare.com/Home.html
Trebovir Hotel [quad, a/c]
VICTORIA STATION AREA:
Cherry Court Hotel [quad, quint]
http://www.cherrycourthotel.co.uk/
Luna Simone Hotel [quad]
http://www.lunasimonehotel.com/
Best Western Victoria Palace [quad]
[They also have apartments according to some reviews on TripAdvisor, but I can’t seem to locate the apartments on their webpage].
http://www.bestwesternvictoriapalace.co.uk/
Melbourne House Hotel [two room family suite]
http://www.melbournehousehotel.co.uk/
Cartref House [quad]
http://www.cartrefhouse.co.uk/
Vandon House [quad, one bedroom apartment]
OTHER AREAS:
Castleton House Apartments [apartments]
http://www.castletownhouse.co.uk/
Marlin Lodge [apartments]
http://www.london-apartment-rental.com/
Griffin House [apartments]
90 Old Church Street, Chelsea [B&B]
http://www.chelseabedbreakfast.com/
Captain Bligh House [studio, apartment]
http://www.captainblighhouse.co.uk/
New Inn Pub
http://www.newinnlondon.co.uk/
Apartment 17 [apartments]
Dalmacia Hotel [inexpensive two bedroom apartments in Shepherd Bush Market area]