Gather your 'tribute' items to be signed together. Letters and photos work best as other heavier items are going to be expensive to ship (note, you are going to have to pay for shipping both TO the UK and also back home here to the USA). Make sure you have included a nice 'fan mail' letter to ROBERT PATTINSON (NOT Edward Cullen; Edward Cullen, though wonderful in every way, is merely a character and to address a letter to the actor where you refer to the CHARACTER and NOT the 'real person' may be taken as an insult), your 'tribute' item (or items), either a self addressed envelope with proper postage on it and your return address OR several international reply coupons (which can be purchased at any united states postal service office--they will explain what they are, the cost, how to use them, etc.)
Pack everything carefully so that nothing gets bent, creased, broken, or ruined. Address your box/envelope (minimum size of your shipping and return envelope should be at least 8.5 X 4, larger is always a little better though) to the following: ATTN: Robert Pattinson
c/o: Curtis Brown Group Ltd. Haymarket House 5th floor
28-29 Haymarket London SW1Y 4SP ; make sure that your personal information on your shipping envelope/box as well as on the return one is clearly legible in bold black ink; and don't forget to include a 'pre thank you' in your fan letter; thanking him for taking time out of his schedule to correspond with you.
Have patience. He has thousands of fan letters, emails, interviews, etc. to do constantly now (thanks to Twilight--and don't forget that the production of NEW MOON is now underway as well! So he's a busy guy!) He lives in the UK; so letters/responses back to the USA are taking upwards of 4-5 months right now! Good luck!