Joung
Jakarta
What are the best, comfortable hotels in London that are cheap?
Tune Hotel - Westminster, London is in a great location (King's Cross), comfortable and well-priced. http://double-barrelledtravel.com/review-tune-hotel-london/
Also check out Airbnb.
I second using Hotwire.com. If you're willing to wait til the last minute, you might find some great deals. (I usually filter on hotels that have > 90% recommendation ratings.) Also keep an eye on the The Hoxton, Shoreditch and The Hoxton, Holborn for deals on their website.
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London is notoriously expensive for hotels, especially if you want to stay somewhere nice and also central. We usually use the websites www.laterooms.com or www.lastminute.com to find a deal. These hotels are good and are in decent locations: Lime Tree Hotel Xenia Hotel and Artist Residence London You can walk to nearby underground stations and there are lots of facilities nearby.
Have a good trip.
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We have had great luck using www.vrbo.com. We rented a full 2 bedroom flat just outside of downtown London for less than half the cost of a small hotel room. Only downside it was a 5 minute walk to the underground "Metro" Station and 20 minute ride to central London. VRBO stands for "VACATION RENTALS BY OWNER"
I recommend the Hampton by Hilton London Waterloo there. Very affordable but gives you free wifi, free continental breakfast as part of your rate. Plus you should join HiltonHHonors their loyalty program (you can sign up online in advance) and you get to choose your room and leverage the HHonors app to earn free nights! So not cheap but great value and very nice rooms, public spaces, people are friendly and you get free points!
The Premier Inn chain has hotels in good locations. The rooms are pretty basic and very little by way of amenities, e.g. room service, fitness facilities, but the cost is budget level for London. Or try vacation rentals like Home Away. We've had some very good flats at prices better than most hotels.