Dear Sir/Madam, 

I am writing  with regard  because I am looking for accommodation for my  tow   two-month stay ing  in London,   starting  next month.

I am a high school student from Beijing, China, and my name is Mike Wang. Because I applied  for  a training course in London University three months ago, I will  take  start  it in August. I noticed from the Internet that your agency is close to the university  where  I am going to take my course [1], so I  wish  hope  you can recommend an apartment for me. Because I am longing  for  to  practise my English, I hope I can stay with some  natives  locals  so that I can communicate with them in English. A room with  a  bed and  a  desk is the basic requirement, and there should be a Wi-Fi connection because I will talk to my parents everyday on  s  Skype. The  P  price should be around £ 500 per month and it will be better if it is lower.

I will arrive  in  London on August 11. I am looking forward to hearing from you as soon as possible.

Yours sincerely, 
Mike Wang

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[1] Here is the corrected version of two sentences:

Because I applied for a training course in London University three months ago, I will start it in August. I noticed from the Internet that your agency is close to the university where I am going to take my course.

Because the first sentence identifies the university and states that you will be taking a course there, you don't need to repeat this information in the second sentence.  Therefore, we can further edit your letter as follows:

Because I applied for a training course in London University three months ago, I will start it in August. I noticed from the Internet that your agency is close to the university where I am going to take my course.