Unclear GET request mixed values
When you send a GET request in HTTP you get a HTTP response back, not just the contents of the file you requested.

For instance, your request may result in a response of:

HTTP/1.1 200 OK
Date: Thu, 28 Dec 2017 11:02:21 GMT
Server: Apache/2.4.25 (Ubuntu)
Last-Modified: Wed, 05 Apr 2017 09:40:30 GMT
ETag: "2c39-54c682ee19688"
Accept-Ranges: bytes
Content-Length: 3
Vary: Accept-Encoding
Connection: close
Content-Type: text/plain

1


As you can see there's plenty of occurrences of 0 and 1 in there to trigger your LED. 

You need to parse the incoming data better. Read it line by line and only start reacting to the content after the blank line that indicates the division between header and body.