Hi,
Some years ago, my British teacher marked as wrong my closing sentence in a letter (FCE level) to a friend. I had witten "Please write me soon." 
I was then taught that British and American English differ on this (... write you => AmE; ... write to you => BrE).
Here are three extracts from three dictionaries.
* 1 *
to send a letter or similar message to someone, giving them information or expressing your thoughts or feelings:
She hasn't US written me/UK written to me recently.
SOURCE: Cambridge online dictionaries
* 2 *
to put information, a message of good wishes, etc. in a letter and send it to sb:
She wrote to him in France. (...)
I wrote a letter to the Publicity Department. (...)
(NAmE) Write me while you’re away.
(NAmE) He wrote me that he would be arriving Monday.
SOURCE: Oxford dictionary
* 3 *
to write a letter to someone
write to I've written to my MP, and to the city council.
write somebody American English Chris hasn't written me for a long time.
I wrote her several letters, but she didn't reply.