The Wardonia Hotel (basic, no frills rooms), 46-54 Argyle Street London, I found in both Google Map Search for hotels near the King's Cross tube station (2 block) and within proximity to the British Library (2 blocks away). It was also recommended by a forum post on Rick Steve's website.
It was 50 Pounds per night, versus the St. Pancras Hotel across the street from King's Cross tube Station which was 250 Pounds per night (luxury). I was in a single, basic room, with a bed, en suite bathroom and shower, cable TV, free WiFi in the room (be careful when booking accommodations anywhere to check to see if WiFi is in the room or if you have to go to the lobby/pub, etc to get it.) It also had a terrific view of the clock tower of St. Pancras Station from my window. It's a quiet street, set two short blocks from the tube station.
It takes an hour on the Picadilly line (no changes) from Heathrow. That's the least expensive way to get there from Heathrow, and easy to get an Oyster card (put money on the card, and just swipe to enter the station, swipe at destination, and put money on the card as needed),
The rooms at the Wardonia are clean, and I really liked the fact that they had someone manning the front desk 24/7. The staff is helpful, and they have a display rack of brochures, some of which offer discounts to attractions. There is a grocery store in St. Pancras station, several mom and pop shops with fresh fruit nearby (the best time to go is around 4 or 5 pm when they're discounting the day's produce).
There is no elevator, but they will help get you upstairs if you have heavy luggage. The rooms are not large, but they are comfortable. For the purpose of this review, they do not have a swimming pool or restaurant, but there are plenty of restaurants, including the British Library cafe, and O'Neill's Pub, a Burger King, A Subway Restaurant, and a McDonald's in short walking distance.
Rooms facing back have less street noise. But, it's offset from the main road, Eustan Street by...
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This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.