Some hotels have a set Early Arrival Rate to cover these kinds of situations, others will let you buy an extra night even if you don't check in until the next morning. E-mail or call the reservations dept. of the hotel directly to arrange the surcharge to guarantee availability. Don't depend upon the worldwide 800# to do it if not having early access to the room is a deal breaker or would cause other problems.

Another possibility: The Yotel at Heathrow will accept reservations for arrival at any hour of the day or night for a minimum of 4 hours. The rate I found for a random date in December was £32, tax included.

http://www.yotel.com/hotels/london-heathrow