The Grand Divan restaurant on the ground floor is certainly a luxurious place to eat breakfast. It was eerily deserted at first, but slowly began to fill with a few customers as the 9am witching hour approached. The food was good, and not prohibitively expensive, although the serving staff did have a frustrating habit of bringing things that were not ordered, which subsequently appeared on the bill. All in all, it was a good place to breakfast though, and the best thing about eating early is that things can be kept relatively inexpensive even in the grandest settings in London, as wine is not on the menu.
For more, see http://www.simpsonsinthestrand.co.uk/