cheap 1 adult flight from london to hk on 20-21/7?

Sorry, but you will not find anything below or even at £600, because first, you are leaving in four-five days, second, you are leaving on the weekend, the most expensive time to fly, and third, your specifications are hard to come by under £1,000.

However, the cheapest, most logical itinerary I could find is outlined below:
TOTAL COST: £1,107/person
Airline: Qatar Airways
Duration: 20/7 (Saturday) - 1/8 (Thursday)
Website: http://skyscanner.com
London-Heathrow -------- 2130 --------- Hong Kong ------------ 2120 (+1) ------- via Doha
Hong Kong ----------------- 0120 --------- London-Heathrow --- 1315 -------------- via Doha

Keep in mind:
* The sooner you book, the cheaper the fares
* If you can arrive on 1/8 past 1800, say at 2100 instead, you can save nearly £250
* If you can depart sometime during the week, fares can be considerably cheaper
* Use the filters in the left-hand column to specify that you want to return before 1800
* Leaving on 20/7 Sat. seems to be more ideal than leaving on 21/7 Sun.

Good luck!