Jetlag is worse travelling east. So you are likely to be more affected by it travelling from the UK to the Far East, or back to the UK from the USA, than the other way round.
Can you do anything to minimise it? There are several schools of thought:

Switch to the sleeping and eating schedule of your destination

Ideally you should start a few days BEFORE you travel. Gradually adjust your bedtimes and waking times to the destination time zone before leaving on your trip. If traveling eastward, this means going to sleep one hour earlier than normal on day one and waking up one hour earlier. On day two, bedtime would be two hours earlier and waking up time would be two hours later. On the third day, bedtime would be three hours earlier and wake time would be three hours earlier. If it's not possible to follow this gradual schedule, some people suggest pre-adjusting to the new time zone a day in advance, by setting your watch to your destination time the day before you travel and preconditioning yourself to the new time.
A sleeping pill for a night or two may make it easier to sleep on the plane and adjust to the new time zone. Use short-acting sleeping pills like Sonata or Ambien.
If you need to have a nap at the "wrong" time, experienced travellers suggest limiting naps to no more than an hour.

Diet

The "Anti-Jet-Lag Diet," developed by Dr. Charles F. Ehret of Argonne National Laboratories, alternates days of "feasting" on high-protein breakfasts and lunches and high-carbohydrate dinners with days of "fasting" on small, low-calorie meals. Start by feasting on the fourth day before arriving at your destination, then fast on the third day, feast on the second, and fast one day before. During the first three days, drink beverages which contain caffeine only between 3 and 5 pm. On the day before arrival, however, you should drink caffeine in the morning for a westbound flight or between 6 and 11 pm for an eastbound flight. Do not drink alcohol on the plane.

Light/Melatonin

Our bodies get clues about what time of day it is from the amount of light. This technique uses light to reset the body clock, because light has the ability to inhibit the production of a brain hormone, melatonin, that triggers sleep. If you are travelling from west to east, on arrival avoid the sun for the rest of the day. The next morning, take a walk outdoors in the sunshine. Avoid wearing sunglasses when outdoors during the first few days, and keep lights on indoors during the daytime.
Melatonin supplements are thought to help the body quickly adjust to the new surroundings. The recommendation is to take a 0.5 mg tablet of melatonin a night for three nights, one hour before normal bedtime, AFTER arrival in your destination.

Homeopathy

The most popular homeopathic remedy for Jet Lag is a product called "No Jet Lag". It contains tiny (homeopathic) amounts of arnica montana (Leopard's bane), bellis perennis (Daisy), Chamomilla (Wild chamomile), Ipecacuanha (Ipecac), and Lycopodium (Clubmoss).

All advisors agree that drinking plenty of water and avoiding caffeine and alcohol during your flight will minimize dehydration, which exacerbates jet lag.