We were stuck several years ago with no reservations having just arrived xmas day (party of 7) and were staying around hyde park corner. The Hard Rock Cafe took pity on us and squeezed us in, and even they had a special menu, pricey and closed early, but it worked and we still laugh about that dinner. boxing day is only marginally better. One option for that day is sofra a multi location turkish restaurant that is is shepherd's market or st christopher's place. Its not expensive and food is good.