And if you want to be hyperliteral about the sentences (masaegu's translation is more correct, but this will sort of show the meaning behind the bits of the sentence),
下手な日本語で失礼します。 = I commit offense/am impolite due to my poor Japanese.
下手な日本語でお許しください。 = Would you please permit/forgive me for my poor Japanese?

I have to admit, I'm not sure whether to classify the で as the particle or as the てform of だ here. I assumed it was the particle (for some reason), but if it's the てform of the copula then they are slightly different in literal translation:

The Japanese is bad [in this letter], so I commit offense/am impolite/am sorry.
The Japanese is bad [in this letter], so would you please permit/forgive it/me?

What could be some alternative ways to say this that'll make it sound more native? From asking around a few places on the internet, I've gotten the following possibilities:

____________ と申します。

____________ といいます。

Could either of these be used? Would you say either of them is better than '私の名前はリアムです。'?

HERE IS MY FINAL DRAFT:


(AUTHOR NAME) さまへ

私の名前はリアムです。19歳のイギリス人の男性です。
去年日本に行った時に、「(TITLE)」の日本語の本を買い� �した。　イギリスに帰ってから、読みました。
とても、とても素晴らしい本だと思いました！それから 、(TITLE)は私の一番好きな本になりました。

次に日本に行く時に、(AUTHOR SURNAME)先生に会いたいと思いますが、(AUTHOR SURNAME)先生はたぶんとてもお忙しいでしょうね。

下手な日本語でお許しください。

読んでいただいてありがとうございます！
リアム


Does this look alright? :D
I'm hoping to send it tomorrow

EDIT: If there are the question marks in diamonds again, they're once again supposed to be 'ま'

Thanks for sharing it with me, KyleGoetz san. :)

In both cases, it is a particle.

Use the first one. The second one is too conversational.

Looks good. Don't worry about not sounding like a Japanese-speaker. It will be more personable that way.

Lol hey there Liam! I'm AnonStudent from Y!A :D Glad to see you took my advice. Did you make an account on Lang-8 too?

Also, Mr. Masaegu, since he's trying to say "I bought the Japanese language (version) of your book, (TITLE)." wouldn't ”「(TITLE)」の日本語版を買いました。” be a closer translation? Just curious ;)

Of course, it would, Ms. SP.

I didn't change it because my basic opinion is that unless there are parts where you are unintentionally saying something that could offend the reader, you should send your letter as is even with the mistakes and unnaturalness. This is why I only changed two parts in my first post. If I were the manga-ka, I don't think I would appreciate a letter in perfect Japanese from England. I would know immediately that it wasn't written by the fan himself.

Thanks. :)
That's a good thing to hear. As I've never lived in Japan or been anywhere near a Japanese district, I wasn't expecting it to sound native. If it did... I would be gob-smacked! XD

It looks like all the corrections I got are relatively minor, and I'll learn them now that I know where I went wrong. :p