We've scanned every flight from Southampton to Tokyo to find the best deals. If you want a cheap flight, it's best to be as flexible as you can on dates. If that day's no good for you, try searching by month to see some alternative dates.
New Tokyo International Airport is just one of the airports in Tokyo. If you're not set on a specific airport, try changing your search from New Tokyo International Airport to Tokyo to see a broader range of flights – they might be cheaper.
If you're planning on going to Tokyo during this time, you could take a look at other airport options. Or you could try to get a last-minute bargain.