If it's just regular letters and post cards, you can drop them into any mailbox inside the Disneyland park. Cast members will gather the items and mail them for you. As for a reglar post office, closest is at 1180 W Ball Rd, which is at the extreme northwest end of the resort area, a block north of the Mickey and Friends parking structure.
Thanks, I will be sending cards and letters but I might want to send some packages also. I think I read somewhere you can send items USP from the Anaheim visitor center but I'm not sure how much they would charge for sending items back to the UK?